Grade 6 Workbook — Chapter 10: The Coordinate Plane

SOL 6.MG.3 · Companion to Textbook Chapter 10

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/.

PAGE 1 — Chapter opener

Chapter 10 · The Coordinate Plane

Standard 6.MG.3

In this chapter you will:

• Label the axes, origin, and quadrants
• Name the quadrant or axis a point sits on
• Graph ordered pairs in all four quadrants and on the axes
• Name ordered pairs from a graph
• Use coordinates to find distance from an axis and between points
• Draw polygons from vertices and find horizontal and vertical side lengths

Words to know: coordinate plane · $x$-axis · $y$-axis · origin · quadrant · ordered pair · vertex

Every coordinate in this chapter is an integer. No calculator needed.

PAGE 2 — Parts of the plane

10.1 Parts of the Coordinate Plane

FIGURE: fig1-coordinate-plane-parts.png (full width)

[Coordinate plane from $-6$ to $6$ on both axes, gridlines at every integer, arrowheads on all four ends, the $x$-axis and $y$-axis labeled, and the origin marked and labeled $(0, 0)$.]

Fill in the blanks.

The horizontal number line is the ____________.

The vertical number line is the ____________.

The point where the two axes cross is the ____________, written as the ordered pair ( ____ , ____ ).

In the ordered pair $(x, y)$, the first number tells you how far ____________ and the second number tells you how far ____________.

Label the diagram. On the figure above, write the words x-axis, y-axis, and origin in the correct places.

Explain. Why are $(2, 9)$ and $(9, 2)$ different points?

PAGE 3 — The four quadrants

The Four Quadrants

FIGURE: fig2-quadrants.png (full width)

[Coordinate plane from $-6$ to $6$ with each of the four regions shaded a different pale color and labeled with a Roman numeral I–IV, counterclockwise from the upper right, with the sign pattern printed inside each region.]

Complete the table.

True or false. A point on an axis is in a quadrant. ______

Explain: _______________________________________________

PAGE 4 — Exit ticket 10.1

Exit Ticket · Lesson 10.1

Name: ________________________ Date: ____________

1. What is the ordered pair for the origin? ______

2. In $(-9, 4)$, what does the $-9$ tell you to do?

3. Name the quadrant containing $(7, -2)$. ______

4. How can you tell from an ordered pair alone that the point lies on the $x$-axis?

PAGE 5 — Graphing points

10.2 Graphing Ordered Pairs

FIGURE: fig3-plotting-ordered-pair.png (half width, right)

[Coordinate plane showing the point $(4, 3)$ plotted with a dashed arrow right 4 along the $x$-axis and a dashed arrow up 3, each arrow labeled.]

The steps. Start at the ____________. Move ____________ first, then ____________. Mark and label the point.

Describe the moves for each point.

Graph and label these points. $(2, 6)$ · $(-4, 5)$ · $(-6, -2)$ · $(3, -3)$ · $(0, 5)$ · $(-1, 0)$

BLANK GRID: coordinate plane from -8 to 8 on both axes, gridlines at every integer, axes labeled, ticks unlabeled for student use

PAGE 6 — Naming points from a graph

Naming Ordered Pairs

FIGURE: fig4-points-in-all-quadrants.png (full width)

[Coordinate plane from $-6$ to $6$ with six labeled points: A at $(3, 5)$, B at $(-4, 2)$, C at $(-2, -3)$, D at $(5, -4)$, E at $(0, 4)$, F at $(-6, 0)$. Only the letters appear on the figure.]

Write the ordered pair for each point.

Write the ordered pair.

A point 3 units right of the origin and 9 units down: ______

A point 7 units left of the origin, on the $x$-axis: ______

Find the error. Priya plots $(0, 7)$ by moving 7 units right. What did she do wrong, and where does the point really go?

PAGE 7 — Exit ticket 10.2

Exit Ticket · Lesson 10.2

Name: ________________________ Date: ____________

1. Describe the moves that graph $(-6, 3)$.

2. A point is 2 units left and 8 units down from the origin. Write its ordered pair. ______

3. Write the ordered pair for a point on the $x$-axis, 5 units right of the origin. ______

4. Why must you move horizontally before vertically?

PAGE 8 — Quadrant or axis

10.3 Quadrants and the Axes

Ask two questions, in order.

1. Is either coordinate zero? If yes, the point is on an axis.
2. If not, what are the two signs? That gives the quadrant.

Remember: a $y$-coordinate of $0$ puts the point on the $x$-axis. An $x$-coordinate of $0$ puts the point on the $y$-axis.

Name the location of each point.

Write one ordered pair of your own for each.

Quadrant I: ______ Quadrant II: ______ Quadrant III: ______ Quadrant IV: ______

On the $x$-axis: ______ On the $y$-axis: ______

PAGE 9 — Sorting points

Sort the Points

Write each point in the correct column.

$(2, 2)$ · $(-5, 1)$ · $(0, -4)$ · $(-6, -6)$ · $(9, -1)$ · $(3, 0)$ · $(-1, 7)$ · $(0, 0)$

Sign flip. The point $(-3, 6)$ is in Quadrant II.

$(-3, -6)$ is in Quadrant ______ because ____________________________

$(3, 6)$ is in Quadrant ______ $(3, -6)$ is in Quadrant ______

Apply it. In a game, the character starts at the origin. Right and up are positive. The character ends at $(-12, -5)$. Describe the position in words.

Quadrant: ______

Challenge. Dante says every point with a $0$ in it is the origin. Give a counterexample and explain.

Counterexample: ______ Explanation: _______________________

PAGE 10 — Exit ticket 10.3

Exit Ticket · Lesson 10.3

Name: ________________________ Date: ____________

1. Name the quadrant of $(-7, 4)$. ______

2. Name the location of $(0, 9)$. ______

3. Write an ordered pair in Quadrant IV. ______

4. Why does a $y$-coordinate of $0$ put a point on the $x$-axis and not the $y$-axis?

PAGE 11 — Distance from the axes

10.4 Coordinates Are Distances

FIGURE: fig5-distance-from-axes.png (right half of page)

[Coordinate plane with the point $(-6, 3)$ plotted, a dashed horizontal segment to the $y$-axis bracketed and labeled "6 units", and a dashed vertical segment to the $x$-axis bracketed and labeled "3 units".]

$$\text{distance from the } y\text{-axis} = |x| \qquad \text{distance from the } x\text{-axis} = |y|$$

Complete the table.

Circle the point that is farther from the $x$-axis: $(3, -8)$ or $(-9, 6)$

Why? _______________________________________________

PAGE 12 — Distance between two points

Horizontal and Vertical Distance

FIGURE: fig6-horizontal-vertical-distance.png (full width)

[Coordinate plane showing a horizontal segment joining $(-3, 4)$ and $(5, 4)$ labeled "8 units" with the note "same $y$-coordinate", and a vertical segment joining $(2, -5)$ and $(2, 3)$ labeled "8 units" with the note "same $x$-coordinate".]

Same $y$-coordinate → horizontal line → distance $= |x_1 - x_2|$ Same $x$-coordinate → vertical line → distance $= |y_1 - y_2|$

Find each distance. Show the subtraction.

Move from a point.

$R$ is at $(2, 3)$. The point 6 units below $R$ is ______

$M$ is at $(-1, -4)$. The point 9 units left of $M$ is ______ The point 5 units above $M$ is ______

$P$ is at $(-3, 6)$. The point 8 units right of $P$ is ______

Find the error. Amara says the distance between $(-4, 3)$ and $(6, 3)$ is $2$ because $6 - 4 = 2$. What went wrong, and what is the correct distance?

PAGE 13 — Exit ticket 10.4

Exit Ticket · Lesson 10.4

Name: ________________________ Date: ____________

1. How far is $(-7, 5)$ from the $y$-axis? ______

2. Find the distance between $(3, -6)$ and $(3, 4)$. ______

3. $T$ is at $(5, -2)$. Name the point 7 units to the left of $T$. ______

4. How can two ordered pairs tell you the points share a horizontal line?

PAGE 14 — Polygons from vertices

10.5 Polygons in the Coordinate Plane

FIGURE: fig7-rectangle-vertices.png (half width, right)

[Coordinate plane with rectangle $A(-3, 2)$, $B(4, 2)$, $C(4, -1)$, $D(-3, -1)$ drawn and its vertices labeled; the top side labeled "7 units" and the right side labeled "3 units".]

Rectangle $ABCD$ above.

Length of $\overline{AB}$: $|\ \ \ \ - \ \ \ \ | =$ ______

Length of $\overline{BC}$: $|\ \ \ \ - \ \ \ \ | =$ ______

Perimeter: ______ Area: ______

Plot the vertices, connect them in order, and answer.

Rectangle with vertices $(-6, 3)$, $(2, 3)$, $(2, -4)$, $(-6, -4)$

BLANK GRID: coordinate plane from -8 to 8 on both axes, gridlines at every integer

Horizontal side: ______ Vertical side: ______ Perimeter: ______ Area: ______

PAGE 15 — Missing vertices and triangles

Missing Vertices

Find the fourth vertex of each rectangle.

Right triangles. A triangle has vertices $(-3, 6)$, $(-3, -2)$, and $(4, -2)$.

Vertical side length: ______ Horizontal side length: ______

Why can't you find the third side with these tools?

Apply it. A community garden has corners at $(-7, 2)$, $(5, 2)$, $(5, -3)$, $(-7, -3)$. Each unit is one yard, and fencing costs $4 per yard.

Perimeter: ______ yards Total cost: $______

Challenge. Kai says the distance between $(-2, 5)$ and $(4, 1)$ is $6$ because $|4 - (-2)| = 6$. Explain why that method does not work here.

PAGE 16 — Exit ticket 10.5

Exit Ticket · Lesson 10.5

Name: ________________________ Date: ____________

1. How long is the side joining $(-5, 2)$ and $(6, 2)$? ______

2. A rectangle has vertices $(0, 0)$, $(9, 0)$, $(9, 5)$, $(0, 5)$. Find its area. ______

3. Three vertices of a rectangle are $(3, 8)$, $(3, 1)$, $(-2, 1)$. Name the fourth. ______

4. How can coordinates alone tell you a side is vertical?

PAGE 17 — Chapter 10 review, part 1

Chapter 10 Review

Part A · Axes, origin, quadrants

1. Horizontal axis: ____________ Vertical axis: ____________ They meet at the ____________

2. Quadrants in order from the upper right, with sign patterns:

   I ( ____ , ____ ) II ( ____ , ____ ) III ( ____ , ____ ) IV ( ____ , ____ )

3. Why is the origin in no quadrant? _______________________________________________

4. On the grid below, label both axes, the origin, and all four quadrants.

BLANK GRID: coordinate plane from -6 to 6 on both axes, gridlines at every integer

Part B · Locating a point

5. Name the location: a) $(-5, 9)$ ______ b) $(3, -12)$ ______ c) $(0, -7)$ ______ d) $(-1, -1)$ ______ e) $(14, 0)$ ______

6. A point in Quadrant II: ______ A point in Quadrant IV: ______

7. A point has a positive $x$-coordinate and $y$-coordinate $0$. Where is it?

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Part C · Graphing

8. Graph and label: $(4, 4)$ · $(-2, 6)$ · $(-5, -3)$ · $(1, -7)$ · $(0, 3)$ · $(-6, 0)$

BLANK GRID: coordinate plane from -8 to 8 on both axes, gridlines at every integer

9. Describe the moves that graph $(-9, -2)$: _______________________________________________

PAGE 18 — Chapter 10 review, part 2

Chapter 10 Review (continued)

Part D · Naming ordered pairs

10. Using fig4-points-in-all-quadrants.png from page 6, name the ordered pairs for A ______, C ______, and F ______

11. A point 6 units left and 4 units up from the origin: ______

12. A point on the $x$-axis, 10 units right of the origin: ______

Part E · Distance

13. Distances from each axis: a) $(-8, 3)$ → $y$-axis ______, $x$-axis ______ b) $(6, -15)$ → $y$-axis ______, $x$-axis ______

14. a) $(-4, 7)$ to $(9, 7)$: ______ b) $(-2, -6)$ to $(-2, 5)$: ______

15. $W$ is at $(-3, -8)$. The point 11 units right of $W$ is ______

16. How do two ordered pairs show the points share a vertical line?

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Part F · Polygons

17. Rectangle $(-5, 6)$, $(4, 6)$, $(4, -2)$, $(-5, -2)$:

    Horizontal side ______ Vertical side ______ Perimeter ______ Area ______

18. Fourth vertex for $(2, -1)$, $(2, 7)$, $(-6, 7)$: ______

19. Triangle $(1, 9)$, $(1, 2)$, $(10, 2)$: vertical side ______ horizontal side ______

Part G · Application and reasoning

20. Gate $(-6, 0)$, pond $(-6, -5)$, playground $(2, -5)$.

    Gate to pond: ______ blocks Pond to playground: ______ blocks Playground quadrant: ______

21. Pool deck $(-4, 3)$, $(6, 3)$, $(6, -4)$, $(-4, -4)$, one unit per meter.

    Area: ______ sq m Railing: ______ m

22. Why is $(0, -9)$ nine units from the $x$-axis but zero units from the $y$-axis?

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23. Two points share a $y$-coordinate and are 14 units apart. One is $(-5, 3)$. Name both possibilities for the other.

    ______ and ______

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 grids: pages 5, 14, and 17 need an unlabeled coordinate plane from $-8$ to $8$ on both axes with gridlines at every integer and arrowheads on all four ends
• Figure widths: fig1, fig2, fig4, fig6 full width; fig3, fig5, fig7 half width placed right
• Grid squares: keep every grid square at least 0.25 in so students can plot and label without crowding
• Answer blanks: keep every blank on the same line as its prompt so the Canva text box does not reflow