Distance on the Coordinate Graph

Multiple Choice

Tamara’s and Gabby’s frogs sit back to back at the point 0 on a number line. Tamara’s frog hops eight units to the right while Gabby’s frog hops 11 units to the left. On what point are each frog now sitting?

• Tamara’s: -5, Gabby’s: 1
• Tamara’s: 8, Gabby’s: -11
• Tamara’s: -2, Gabby’s: 4

Match

Using the coordinate plane, match the equations to the distances between the listed points.

• The distance between A and B.

• The distance between A and C.

• The distance between B and C.

• $$\left|-5\right|+\left|1\right|=6$$

• $$\left|-7\right|+\left|3\right|=10$$

• $$\left|1\right|+\left|-5\right|+\left|3\right|+\left|-7\right|=16$$

Multiple Choice

Tamara’s and Gabby’s frogs sit back to back at the point 0 on a number line. Tamara’s frog hops eight units to the right while Gabby’s frog hops 11 units to the left. Who's frog jumped the furthest?

• Tamara’s frog
• Gabby’s frog

Graphing

Carter made a map of his neighborhood on a coordinate plane and located his house at the point (-8, -7). Izabella lives 9 miles away from Carter.

Izabella's house and Carter's house have the same x-coordinates but are in different quadrants. Plot two points on the coordinate plane to represent Izabella's house and Carter's house.

Multiple Choice

Tamara’s and Gabby’s frogs sit back to back at the point 0 on a number line. Tamara’s frog hops eight units to the right while Gabby’s frog hops 11 units to the left. How far apart are the two frogs now?

• 7 units
• 11 units
• 19 units

Graphing

Izabella's house is located at (-8, 2). Sam lives 12 miles away from Izabella.

Izabella's house and Sam's house have the same y-coordinates but are in different quadrants. Plot two points on the coordinate plane to represent Izabella's house and Sam's house.

Multiple Choice

Tamara’s and Gabby’s frogs sit back to back at the point 0 on a number line. Tamara’s frog hops eight units to the right while Gabby’s frog hops 11 units to the left. Represent the distance between the two frogs, 19 using absolute value.

• |-11 + -8|
• |10 + 9|
• |1 + 9|

Math Response

Use the graph to answer the following question.

What is the distance between Shannon Ranch and Starbucks?

Type answer here

Correct Answer: 9

Deg^°

Rad

Multiple Choice

What is the distance between the pair of points (-5, 7) and (8, 7)?

• 10
• 2
• 13

Multiple Select

Use the coordinate plane to determine whether each statement about the vertices (points) of the triangles is true or false.

(Select ALL of the statements that are TRUE.)

• The distance from A to D is $$-3+3$$

• The distance from E to F is $$\left|-7\right|-\left|-3\right|$$

• The distance from B to E is $$\left|-6\right|+\left|6\right|$$

• The distance from C to F is $$\left|-6\right|+\left|7\right|+\left|6\right|$$

• The distance from A to F is $$\left|7-3\right|+\left|3+6\right|$$

Multiple Choice

What is the distance between the pair of points (-5, 7) and (-5, -3)?

• 10
• 8
• 6
• 4

Multiple Choice

Using the coordinate plane to answer the questions. Each unit on this coordinate plane represents 1 kilometer. Nathan rode his bike from his house to Dylan's house. How many kilometers did he ride his bike?

• -5 kilometers

• 5 kilometers

• 9 kilometers

• 10 kilometers

Multiple Choice

Point A has coordinates (5, 2). Name one point that is a distance of eight units away from point A.

• (3, -1)
• (4, -11)
• (10, -2)
• (-3, 2)

Multiple Choice

If Nathan adds the y-coordinates for the points of Dylan's and Gio's houses, plus the x-coordinates of his and Dylan's houses, he will get the total distance that he rode.

Which equation could be used to find the total distance Nathan traveled on his bike?

• $$\left(\left|-5\right|+\left|5\right|\right)+\left(\left|-5\right|+\left|2\right|\right)$$

• $$\left(\left|7\right|+\left|10\right|\right)+\left(\left|10\right|+\left|7\right|\right)$$

• $$\left(\left|-5\right|-\left|5\right|\right)+\left(\left|7\right|-\left|-2\right|\right)$$

• $$\left(\left|2\right|+\left|-5\right|\right)+\left(\left|10\right|+\left|7\right|\right)$$

Multiple Choice

• points A and C
• points B and D
• points C and D

Graphing

Julian moves into a house that is 12 kilometers west of Gio's house and 9 kilometers north of Nathan's house. Identify the location of Julian's new house.

Multiple Choice

• Points B and E
• Points A and D
•  Points C and E

Multiple Select

Use the coordinate plane to determine whether each statement about the coordinates is true or false.

(Select ALL of the statements that are TRUE.)

• Shannon Ranch is located directly across the y-axis from In-n-Out and is on the same y-coordinate as In-n-Out.

• The distance between Starbucks and Green Acres MS is equal to the distance between Riverway Sports Park and In-n-Out.

• Shannon Ranch is further from Starbucks than it is from In-n-Out.

• To find the distance between Riverway Sports Park and Green Acres MS, you can use the equation: $$\left(\left|7\right|+\left|-6\right|\right)+\left(\left|6\right|-\left|-2\right|\right)$$

• If A & W were plotted at $$\left(-3,-2\right)$$ it would the same distance from Shannon Ranch to A & W as the distance of A & W to Starbucks.

Multiple Choice

Antoine, the active ant, sits on a number line at the position of the number 8. Antoine walks 3 steps in the positive direction, 12 steps in the negative direction, and 6 step in the positive direction. At this number, Antoine sits down and takes a nap. What number is he at?

• 3
• 22
• 5

Drag and Drop

Sam wants to find the distance between the points (-2 , -5) and (-2 , -10). She says that because $$\left|-5\right|+\left|-10\right|=15$$ , the distance is 15 units. Is Sam correct?

To find the distance using absolute values, first Sam should find the absolute values of the ​

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of the points. The points are located ​

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, so she should ​

Placeholder

the absolute values to find the distance between the points. The distance between the two points is ​

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. Sam is ​

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.

Drag these tiles and drop them in the correct blank above

y-coordinates

in the same quadrant

subtract

5 units

not correct

x-coordinates

in different quadrants

add

10 units

correct

Multiple Choice

• 100 units²
• 60 units²
• 168 units²

Multiple Choice

• 12 units²
• 144 units²
• 48 units²