Distance in the Coordinate Plane

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Teacher Facing
October 16, 2024

Grade 8 Mathematics

Unit 6: Pythagorean Theorem
Lesson 6: Distance on the Coordinate Plane

Do Now

3

Solve for the missing side length of each right triangle.

1.

2.

20

16

34

5

4

LO: SWBAT determine the distance between two points on a
coordinate plane using the Pythagorean theorem.

DOL: Given a set of problems, students will correctly
determine the distance between two points on a coordinate
plane using the Pythagorean theorem in at least 4 of 5
questions.

MATH.8.7D Determine the distance between two points on a coordinate plane using the Pythagorean theorem.

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Academic Vocabulary

a² + b² = c²

b

a

c

legs

hypotenuse

Pythagorean Theorem

6

How would you verify,
without using measuring
tools, that three points

on a coordinate plane
form a right triangle?

I can verify that three points on a coordinate
plane form a right triangle by…

7

Darius wants to find the distance between the two points on the
coordinate plane.

Can we accurately

count between

these two points?

The Pythagorean

theorem can be used to

find the distance

between two points on a

coordinate plane.

8

In order for Darius to find the length of the
segment between the two points, he needs
to make a right triangle.

How long is the vertical leg of the right
triangle?

How long is the horizontal leg of the right
triangle?

9

Darius can now use the length of the legs of
the right triangle in the Pythagorean theorem
equation and solve for the length of the
hypotenuse.

a² + b² = c²

7

6

10

Theron graphed the points (2, 3) and (−4, −7)
on the coordinate plane.
He needs to calculate the distance between
the points he graphed.

Theron needs to…

11

Does it matter if Theron

draws his vertical and

horizontal lines on the other
side of the hypotenuse? Why

or why not?

It does/does not matter if Theron draws the lines on the other side of the hypotenuse
because…

12

Help Theron calculate the distance
between the points he graphed.

What are the lengths of
the legs of the right
triangle?

What does

Theron need to

do next?

13

10

6

Theron can now use the length of the legs of the
right triangle in the Pythagorean theorem equation
and solve for the length of the hypotenuse.

a² + b² = c²

14

Chloe used a computer software to draw the points on the
coordinate plane. What is the distance between the two points?

15

What is the distance between the two points on the
coordinate plane?

A. 2.2 units

B. 7.1 units

C. 3.2 units

D. 9.1 units

16

Ms. Crane graphed points A and B on the grid below. To the
nearest tenth, what is the distance between the two points?

A. 13.8 units

B. 15.4 units

C. 14.4 units

D. 24.1 units

17

Two points on a map can be represented by the
coordinates (6, 10) and (2, 5). Explain how to find the
distance between the points using the Pythagorean
theorem.

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Graph the coordinates (6, 10) and (2, 5). What is the distance
between the points?

19

Park

Store

Colton drives from the store to the park.

What is the distance Colton drives?
Round to the nearest tenth.

20

Liza walks through the mall represented on the diagram.

iMobile

Threadz

Pets
R’ Us

What is the distance Liza walks from Pets R’
Us to iMobile?
Round to the nearest tenth.

A. 3.9 units

B. 14.4 units

C. 19 units

D. 15.5 units

21

iMobile

Threadz

Pets
R’ Us

What is the distance Liza walks from iMobile to Threadz?

A. 12 units

B. 16 units

C. 20 units

D. 36 units

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After leaving Threadz, Liza walks back to Pets R’ Us to leave the mall.

iMobile

Threadz

Pets
R’ Us

What is the distance Liza walks from Threadz
to Pets R’ Us?
Round to the nearest tenth.

A. 9.2 units

B. 12.4 units

C. 15.6 units

D. 13.8 units

23

What is the total distance Liza walks through the mall?

iMobile

Threadz

Pets
R’ Us

A. 39.6 units

B. 41.3 units

C. 47.9 units

D. 40.2 units

24

When determining the distance between two points on a coordinate
plane using the Pythagorean theorem, what effect do negative
coordinates have on calculating the distance?

Questions by Sly from Pixabay