Grade 7 Workbook — Chapter 15: Dilations in the Coordinate Plane

SOL 7.MG.4 · Companion to Textbook Chapter 15

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Item numbers match the textbook exactly.

PAGE 1 — Chapter opener

Chapter 15 · Dilations in the Coordinate Plane

Standard 7.MG.4

In this chapter you will:

• Find the coordinates of a polygon's image after a dilation centered at the origin
• Sketch the image of a dilation on a coordinate grid
• Tell an enlargement from a reduction
• Recognize and describe dilations in scale drawings and graphic design

Words to know: transformation · dilation · preimage · image · prime notation · center of dilation · scale factor · enlargement · reduction · similar

Two rules hold on every page of this chapter. The scale factor $k$ is always $\tfrac14$, $\tfrac12$, $2$, $3$, or $4$. The center of dilation is always the origin, $(0, 0)$.

The rule: a dilation centered at the origin sends $(x, y)$ to $(kx, ky)$. Multiply both coordinates by the same factor.

Drawing convention: preimage = solid outline. Image = dashed outline, labeled with primes ($A'$, $B'$, $C'$).

PAGE 2 — What a dilation does

15.1 What a Dilation Does

FIGURE: fig1-dilation-factor-2.png (full width)

Fill in the blanks.

The figure you start with is the ______________. The figure you end with is the ______________.

The fixed point everything is measured from is the ______________ of ______________. In this chapter it is always the ______________.

A dilation centered at the origin sends $(x, y)$ to ( ______ , ______ ).

A scale factor greater than 1 produces an ______________. A scale factor between 0 and 1 produces a ______________.

A dilation changes ______________ lengths but leaves ______________ measures alone, so the image is ______________ to the preimage.

Guided practice.

1. $\triangle ABC$: $A(1, 3)$, $B(3, 1)$, $C(2, 4)$. Dilate by $k = 2$, center the origin.

   $A'($ ______ , ______ $)$ $B'($ ______ , ______ $)$ $C'($ ______ , ______ $)$

2. Rectangle $PQRS$: $P(2, 2)$, $Q(6, 2)$, $R(6, 4)$, $S(2, 4)$. Dilate by $k = \tfrac12$, center the origin.

   $P'($ ______ , ______ $)$ $Q'($ ______ , ______ $)$ $R'($ ______ , ______ $)$ $S'($ ______ , ______ $)$

PAGE 3 — Enlargement or reduction?

Which Way Does It Go?

FIGURE: fig4-enlargement-vs-reduction.png (full width)

3. Write E for enlargement or R for reduction.

   a) $k = 3$	b) $k = \tfrac12$	c) $k = 4$	d) $k = \tfrac14$

4. A triangle has angles measuring $40°$, $60°$, and $80°$. It is dilated by $k = 4$ about the origin.

   Image angle measures: ______ , ______ , ______

   Why? _______________________________________________

5. A dilation centered at the origin with scale factor $k$ sends $(x, y)$ to ____________.

Independent practice.

6. Dilate by $k = 3$, center the origin.

   a) $(2, 5) \rightarrow$ ( ______ , ______ ) b) $(-1, 4) \rightarrow$ ( ______ , ______ ) c) $(0, -3) \rightarrow$ ( ______ , ______ )

7. Dilate by $k = \tfrac14$, center the origin.

   a) $(8, 12) \rightarrow$ ( ______ , ______ ) b) $(-4, 16) \rightarrow$ ( ______ , ______ ) c) $(20, 0) \rightarrow$ ( ______ , ______ )

PAGE 4 — Polygons and points

Dilating Whole Polygons

FIGURE: fig3-reduction-half.png (full width)

8. $\triangle DEF$: $D(-2, 3)$, $E(4, 1)$, $F(0, -5)$. Dilate by $k = 2$, center the origin.

   $D'($ ______ , ______ $)$ $E'($ ______ , ______ $)$ $F'($ ______ , ______ $)$

9. Quadrilateral $WXYZ$: $W(4, 4)$, $X(8, 4)$, $Y(8, 12)$, $Z(4, 8)$. Dilate by $k = \tfrac12$, center the origin.

   $W'($ ______ , ______ $)$ $X'($ ______ , ______ $)$ $Y'($ ______ , ______ $)$ $Z'($ ______ , ______ $)$

10. A point at $(5, 2)$ has image $(15, 6)$. Scale factor: ______

    How do you know? _______________________________________________

11. Application. A sticker is laid out with corners $(0, 0)$, $(6, 0)$, $(6, 4)$, $(0, 4)$, each unit one centimeter. It is dilated by $k = 2$ about the origin for a window decal.

    Image corners: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

    Decal width: ______ cm Decal height: ______ cm

12. Reasoning. Why is the origin the only point that does not move? Use the rule $(x, y) \rightarrow (kx, ky)$.

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PAGE 5 — Exit ticket 15.1

Exit Ticket · Lesson 15.1

Name: ________________________ Date: ____________

13. Image of $(2, -3)$ under $k = 4$, center the origin: ( ______ , ______ )

14. $\triangle JKL$: $J(6, 2)$, $K(-4, 8)$, $L(0, -6)$; $k = \tfrac12$, center the origin.

    $J'($ ______ , ______ $)$ $K'($ ______ , ______ $)$ $L'($ ______ , ______ $)$

15. Is $k = \tfrac14$ an enlargement or a reduction? ______

    What happens to each point's distance from the origin? _______________________________________________

16. Why is the image of a polygon under a dilation always similar to the preimage?

    Stays the same: _______________________________________________

    Changes: _______________________________________________

PAGE 6 — Why the rule works

Rays from the Origin

FIGURE: fig2-rays-from-origin.png (full width)

Trace it. Lay a straightedge from the origin through $A$. It should pass straight through $A'$. Repeat for $B$ and $C$.

Complete the sentence. The image vertex lies on the ______________ from the origin through the preimage vertex, and its distance from the origin is ______________ by the scale factor.

Check each pair by comparing directions. Write each as rise over run.

Explain. What would go wrong if you multiplied only the $x$-coordinate by $k$?

PAGE 7 — Coordinate tables

15.2 Coordinates of a Dilated Polygon

FIGURE: fig5-table-and-graph.png (full width)

Guided practice.

17. Complete the table for a dilation with $k = 2$, center the origin.

    Preimage	Multiply by $2$	Image
    $A(1, 4)$
    $B(5, 2)$
    $C(3, -3)$

18. $\triangle PQR$: $P(4, 6)$, $Q(10, 2)$, $R(-8, -4)$; $k = \tfrac12$.

    Preimage	Multiply by $\tfrac12$	Image
    $P(4, 6)$
    $Q(10, 2)$
    $R(-8, -4)$

19. $\triangle DEF$: $D(-2, 1)$, $E(0, 4)$, $F(3, -2)$; $k = 3$.

    $D'($ ______ , ______ $)$ $E'($ ______ , ______ $)$ $F'($ ______ , ______ $)$

PAGE 8 — Running the rule backward

Backward and Forward

20. A dilation centered at the origin sends $M(3, 4)$ to $M'(12, 16)$.

    $\dfrac{12}{3} =$ ______ $\dfrac{16}{4} =$ ______ Scale factor: ______

21. A dilation with $k = 2$ produced the image point $A'(10, -6)$. Preimage $A($ ______ , ______ $)$

Independent practice.

22. Dilate by $k = 4$, center the origin.

    a) $(2, 3) \rightarrow$ ( ______ , ______ ) b) $(-1, 5) \rightarrow$ ( ______ , ______ ) c) $(0, -2) \rightarrow$ ( ______ , ______ )

23. Quadrilateral $ABCD$: $A(4, 8)$, $B(16, -4)$, $C(-12, 0)$, $D(20, 8)$; $k = \tfrac14$.

    $A'($ ______ , ______ $)$ $B'($ ______ , ______ $)$ $C'($ ______ , ______ $)$ $D'($ ______ , ______ $)$

24. Quadrilateral $EFGH$: $E(-4, -2)$, $F(2, -2)$, $G(2, 6)$, $H(-4, 4)$; $k = \tfrac12$.

    $E'($ ______ , ______ $)$ $F'($ ______ , ______ $)$ $G'($ ______ , ______ $)$ $H'($ ______ , ______ $)$

25. $\triangle RST$: $R(2, 1)$, $S(5, 3)$, $T(1, 4)$; $k = 3$.

    $R'($ ______ , ______ $)$ $S'($ ______ , ______ $)$ $T'($ ______ , ______ $)$

PAGE 9 — Grid-friendly coordinates

When Fractions Land on the Grid

FIGURE: fig6-quarter-dilation.png (full width)

For $k = \tfrac12$, the preimage coordinates must be even to give whole-number images. For $k = \tfrac14$, they must be multiples of 4.

26. A dilation centered at the origin sends $(6, -4)$ to $(3, -2)$.

    Scale factor: ______ Enlargement or reduction? ______

27. Application. An icon has corners $(0, 0)$, $(4, 0)$, $(4, 4)$, $(0, 4)$. It is dilated by $k = 3$ about the origin for a poster.

    Image corners: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

    Side length before: ______ Side length after: ______

28. Reasoning. A student dilates $(7, 3)$ by $k = \tfrac12$ and gets $(3.5, 1.5)$, then says the answer must be wrong because it is not on a grid intersection.

    Is the arithmetic wrong? ______

    Explain: _______________________________________________

    For $k = \tfrac12$ to give whole numbers, the preimage coordinates must be ______________.

PAGE 10 — Exit ticket 15.2

Exit Ticket · Lesson 15.2

Name: ________________________ Date: ____________

29. Image of $(-5, 3)$ under $k = 2$, center the origin: ( ______ , ______ )

30. $\triangle ABC$: $A(8, 12)$, $B(-16, 4)$, $C(0, -8)$; $k = \tfrac14$.

    $A'($ ______ , ______ $)$ $B'($ ______ , ______ $)$ $C'($ ______ , ______ $)$

31. A dilation centered at the origin sends $(3, -2)$ to $(9, -6)$. Scale factor: ______

32. Why must both coordinates be multiplied by the same factor? What would the image look like if only $x$ were multiplied?

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PAGE 11 — The sketching routine

15.3 Sketching a Dilation

FIGURE: fig7-sketching-steps.png (full width)

The four steps.

• First, plot the preimage and label the vertices.
• Then, multiply every coordinate by $k$ and write the image coordinates down.
• Next, plot the image points and label them with primes.
• Finally, connect the image vertices in the same order as the preimage.

Guided practice.

33. $\triangle ABC$: $A(1, 1)$, $B(4, 1)$, $C(1, 3)$; $k = 2$, center the origin.

    $A'($ ______ , ______ $)$ $B'($ ______ , ______ $)$ $C'($ ______ , ______ $)$

    Sketch both triangles on the grid.

BLANK COORDINATE GRID: x from 0 to 9, y from 0 to 9, unit gridlines, axes labeled x and y (full width)

PAGE 12 — Sketching a reduction

Reductions on the Grid

34. Rectangle $PQRS$: $P(-6, 4)$, $Q(2, 4)$, $R(2, -2)$, $S(-6, -2)$; $k = \tfrac12$, center the origin.

    $P'($ ______ , ______ $)$ $Q'($ ______ , ______ $)$ $R'($ ______ , ______ $)$ $S'($ ______ , ______ $)$

BLANK COORDINATE GRID: x from -8 to 4, y from -4 to 6, unit gridlines (full width)

35. $\triangle DEF$: $D(2, 1)$, $E(3, 3)$, $F(1, 2)$; $k = 3$, center the origin.

    $D'($ ______ , ______ $)$ $E'($ ______ , ______ $)$ $F'($ ______ , ______ $)$

BLANK COORDINATE GRID: x from 0 to 10, y from 0 to 10, unit gridlines (half width)

36. Quadrilateral $WXYZ$: $W(-8, 4)$, $X(4, 4)$, $Y(4, -8)$, $Z(-8, -8)$; $k = \tfrac14$, center the origin.

    $W'($ ______ , ______ $)$ $X'($ ______ , ______ $)$ $Y'($ ______ , ______ $)$ $Z'($ ______ , ______ $)$

BLANK COORDINATE GRID: x from -9 to 5, y from -9 to 5, unit gridlines (half width)

37. Go back to your sketch for item 33. Draw the ray from the origin through $A$ and extend it. Does it pass through $A'$? ______

    What does that confirm? _______________________________________________

PAGE 13 — Independent sketching

Sketch and Label

Fill the table first, then sketch on the grid beneath it.

38. $\triangle JKL$: $J(-2, 1)$, $K(-1, 4)$, $L(3, 2)$; $k = 2$.

    Preimage	Image
    $J(-2, 1)$
    $K(-1, 4)$
    $L(3, 2)$

BLANK COORDINATE GRID: x from -6 to 8, y from -2 to 10, unit gridlines (full width)

39. Quadrilateral $MNPQ$: $M(-4, 6)$, $N(4, 6)$, $P(6, -2)$, $Q(-6, -4)$; $k = \tfrac12$.

    $M'($ ______ , ______ $)$ $N'($ ______ , ______ $)$ $P'($ ______ , ______ $)$ $Q'($ ______ , ______ $)$

BLANK COORDINATE GRID: x from -8 to 8, y from -6 to 8, unit gridlines (full width)

PAGE 14 — More sketching

Bigger Grids, Same Rule

40. $\triangle ABC$: $A(-1, -1)$, $B(2, -2)$, $C(0, 3)$; $k = 3$.

    $A'($ ______ , ______ $)$ $B'($ ______ , ______ $)$ $C'($ ______ , ______ $)$

BLANK COORDINATE GRID: x from -6 to 8, y from -8 to 10, unit gridlines (half width)

41. $\triangle RST$: $R(1, 2)$, $S(2, -1)$, $T(-1, 1)$; $k = 4$.

    $R'($ ______ , ______ $)$ $S'($ ______ , ______ $)$ $T'($ ______ , ______ $)$

BLANK COORDINATE GRID: x from -6 to 10, y from -6 to 10, unit gridlines (half width)

42. Quadrilateral $EFGH$: $E(4, 8)$, $F(12, 4)$, $G(8, -8)$, $H(-4, -4)$; $k = \tfrac14$.

    $E'($ ______ , ______ $)$ $F'($ ______ , ______ $)$ $G'($ ______ , ______ $)$ $H'($ ______ , ______ $)$

BLANK COORDINATE GRID: x from -6 to 14, y from -10 to 10, unit gridlines (full width)

PAGE 15 — Application and reasoning

A Logo on the Grid

43. Application. A triangular logo has vertices $(0, 0)$, $(3, 0)$, $(0, 4)$ on a grid where each unit is one centimeter. Its side lengths are $3$ cm, $4$ cm, and $5$ cm. It is dilated by $k = 3$ about the origin for a window decal.

    Image vertices: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

    New side lengths: ______ cm, ______ cm, ______ cm

BLANK COORDINATE GRID: x from 0 to 12, y from 0 to 14, unit gridlines (full width)

44. Reasoning. A figure's coordinates all lie between $-5$ and $5$. It will be dilated by $k = 4$ about the origin.

    The grid must run from ______ to ______ in both directions.

    Why does checking this first save time? _______________________________________________

PAGE 16 — Exit ticket 15.3

Exit Ticket · Lesson 15.3

Name: ________________________ Date: ____________

45. $\triangle ABC$: $A(2, 3)$, $B(4, 1)$, $C(1, -2)$; $k = 2$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

46. $\triangle PQR$: $P(-8, 2)$, $Q(-2, 6)$, $R(4, -4)$; $k = \tfrac12$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

47. Square $(1, 1)$, $(2, 1)$, $(2, 2)$, $(1, 2)$; $k = 3$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

BLANK COORDINATE GRID: x from -10 to 10, y from -10 to 10, unit gridlines (repeat 3 times, small)

48. How does drawing a ray from the origin through a preimage vertex help you check your sketch?

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PAGE 17 — Dilations at work

15.4 Dilations in the World

FIGURE: fig8-graphic-design-resize.png (full width)

Where they show up. Scale drawings · maps · floor plans · model kits · logo resizing · icon export · photo enlargement · projected slides

The dilation test. Divide each new measurement by the matching original. If every ratio is the same, it is a dilation. If any ratio disagrees, it is a stretch, not a dilation.

Guided practice.

49. A $5$ in by $7$ in photo is enlarged by $k = 2$.

    New dimensions: ______ in by ______ in Enlargement or reduction? ______

50. A $12$ px by $16$ px icon is reduced by $k = \tfrac14$.

    New dimensions: ______ px by ______ px Enlargement or reduction? ______

51. Which resize is a dilation? Show the ratios.

    Resize	First ratio	Second ratio	Dilation?
    a) $6$ by $9 \rightarrow 12$ by $18$
    b) $6$ by $9 \rightarrow 12$ by $15$

PAGE 18 — Designing with dilations

Scale Factors in Design

52. A design triangle has vertices $(0, 0)$, $(4, 0)$, $(0, 3)$ with side lengths $4$, $3$, and $5$. Dilate by $k = 3$ about the origin.

    Image vertices: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

    New side lengths: ______ , ______ , ______

53. A rectangle measures $8$ units by $5$ units and is dilated by $k = 2$.

    Original perimeter: ______ New perimeter: ______

Independent practice.

54. A $3$ in by $5$ in photo enlarged by $k = 4$: ______ in by ______ in

55. A $20$ cm by $24$ cm poster reduced by $k = \tfrac14$: ______ cm by ______ cm

56. Dilation or not? Show the ratios, and give the scale factor where it is one.

    Resize	First ratio	Second ratio	Dilation?	Scale factor
    a) $10$ by $14 \rightarrow 5$ by $7$
    b) $10$ by $14 \rightarrow 20$ by $24$
    c) $9$ by $12 \rightarrow 27$ by $36$

PAGE 19 — Real designs on a grid

Logos, Parks, and Signs

57. A logo has corners $(0, 0)$, $(6, 0)$, $(6, 4)$, $(0, 4)$. The designer needs it at half size for a business card. Dilate by $k = \tfrac12$ about the origin.

    Image corners: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

    Describe the change: _______________________________________________

58. A park outline has corners $(0, 0)$, $(8, 0)$, $(8, 12)$, $(0, 12)$, dilated by $k = 2$ about the origin for a trailhead sign.

    Image corners: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

59. Application. A sticker design is $4$ cm wide and $6$ cm tall. It is enlarged by $k = 3$ about the origin.

    	Original	New
    Width	$4$ cm
    Height	$6$ cm
    Perimeter
    Area

    The area was multiplied by ______.

60. Reasoning. A student widens an $8$ in by $10$ in image to $16$ in by $10$ in by dragging a side handle and calls it a dilation.

    Ratios: ______ and ______ Is it a dilation? ______

    What does the image look like as a result? _______________________________________________

PAGE 20 — Exit ticket 15.4

Exit Ticket · Lesson 15.4

Name: ________________________ Date: ____________

61. A $6$ in by $8$ in photo enlarged by $k = 2$: ______ in by ______ in

62. A $16$ px by $24$ px icon reduced by $k = \tfrac14$: ______ px by ______ px

63. Is $5$ by $8 \rightarrow 15$ by $20$ a dilation? Ratios: ______ and ______ Dilation? ______

    Explain: _______________________________________________

64. Describe one dilation you have seen outside math class.

    Preimage: ____________________ Image: ____________________

    Enlargement or reduction? ______

PAGE 21 — Chapter 15 review, part 1

Chapter 15 Review

Part A · Coordinates of a dilated image (7.MG.4a)

65. $(3, -5)$, $k = 2$: ( ______ , ______ )

66. $(-4, 2)$, $k = 3$: ( ______ , ______ )

67. $(10, -6)$, $k = \tfrac12$: ( ______ , ______ )

68. $(12, -8)$, $k = \tfrac14$: ( ______ , ______ )

69. $\triangle ABC$: $A(1, -2)$, $B(4, 0)$, $C(-3, 5)$; $k = 4$.

    $A'($ ______ , ______ $)$ $B'($ ______ , ______ $)$ $C'($ ______ , ______ $)$

70. Quadrilateral $WXYZ$: $W(8, 4)$, $X(16, 8)$, $Y(4, -12)$, $Z(-8, 0)$; $k = \tfrac14$.

    $W'($ ______ , ______ $)$ $X'($ ______ , ______ $)$ $Y'($ ______ , ______ $)$ $Z'($ ______ , ______ $)$

71. A dilation centered at the origin sends $(2, 7)$ to $(8, 28)$. Scale factor: ______

PAGE 22 — Chapter 15 review, part 2

Chapter 15 Review (continued)

Part B · Sketching a dilation (7.MG.4b)

72. $\triangle ABC$: $A(1, 2)$, $B(3, -1)$, $C(-2, 1)$; $k = 2$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

73. $\triangle PQR$: $P(-6, 8)$, $Q(4, 6)$, $R(2, -4)$; $k = \tfrac12$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

74. $\triangle DEF$: $D(2, 0)$, $E(0, 2)$, $F(-1, -1)$; $k = 3$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

75. Quadrilateral $GHJK$: $G(-8, 12)$, $H(8, 8)$, $J(4, -4)$, $K(-12, -8)$; $k = \tfrac14$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

76. Rectangle $(1, 1)$, $(2, 1)$, $(2, 3)$, $(1, 3)$; $k = 4$. Image: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

BLANK COORDINATE GRID: x from -12 to 12, y from -12 to 12, unit gridlines (repeat 5 times, small — sketch items 72 through 76)

77. On your sketch for item 72, draw the ray from the origin through $B$ and extend it. Does it pass through $B'$? ______

    What does that tell you? _______________________________________________

PAGE 23 — Chapter 15 review, part 3

Chapter 15 Review (continued)

Part C · Dilations in context (7.MG.4c)

78. A $4$ in by $5$ in photo enlarged by $k = 3$: ______ in by ______ in Enlargement or reduction? ______

79. A $24$ mm by $32$ mm icon reduced by $k = \tfrac14$: ______ mm by ______ mm Enlargement or reduction? ______

80. Is $7$ by $9 \rightarrow 14$ by $16$ a dilation? Ratios: ______ and ______ Dilation? ______

81. Logo corners $(0, 0)$, $(6, 0)$, $(6, 2)$, $(0, 2)$; $k = \tfrac12$ about the origin.

    Image corners: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ )

    Describe the change: _______________________________________________

82. How is a scale drawing from Chapter 13 related to a dilation? What plays the role of the scale factor?

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PAGE 24 — Chapter 15 review, part 4

Chapter 15 Review (continued)

Part D · Mixed application and reasoning

83. Application. A banner design is $9$ in by $12$ in, enlarged by $k = 4$ about the origin.

    New dimensions: ______ in by ______ in Original perimeter: ______ in New perimeter: ______ in

84. Application. Park outline $(0, 0)$, $(12, 0)$, $(12, 8)$, $(0, 8)$; $k = \tfrac14$ about the origin.

    Image corners: ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) ( ______ , ______ ) Enlargement or reduction? ______

85. Reasoning. Why does the rule $(x, y) \rightarrow (kx, ky)$ produce a genuine dilation? Use the ray from the origin.

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86. Reasoning. Why is the origin the only point that stays put?

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87. Reasoning. A student dilates $(5, 7)$ by $k = \tfrac14$ and gets $(1.25, 1.75)$. Arithmetic error? ______

    Explain: _______________________________________________

88. Reasoning. A $4$ by $6$ rectangle is dilated by $k = 2$ about the origin.

    Feature	Before	After
    Angle measures	four right angles
    Side lengths	$4$ and $6$
    Perimeter
    Area

Canva production notes

• Page size: 8.5 × 11 in, 0.75 in margins
• Type: headings 24–28 pt, body 12–14 pt, answer blanks 14 pt with 1.5 line spacing
• Blank coordinate grids: every grid must have equal unit spacing on both axes. A dilation drawn on a stretched grid is not a dilation, so do not scale a grid to fill a box non-uniformly.
• Grid labeling: label every axis tick on the small grids only at multiples of 2 to avoid crowding; full-width grids label every unit.
• Figure widths: all Chapter 15 figures are landscape and belong at full width, except fig6-quarter-dilation.png, which is square and can sit at two-thirds width.
• Answer blanks: keep the coordinate blanks ( ____ , ____ ) on one line so the Canva text box does not reflow and split a coordinate pair.