Distance and Midpoint Lessons

Distance Formula

Review and Practice

Find the distance between the points (0,0) and (6,8).

To find the distance:

1. Plug in (6) for X₂ and (0) for X₁.

2. Plug in (0) for Y₂ and (0) for Y₁.

3. Simplify your answer to find d.

Pythagorean Theorem Review

​Pythagorean Theorem

Multiple Select

Which of the following shows the correct way to insert the following coordinates into the DIstance Formula?

(3, 4) , (7, 1)

• $$d\ =\ \sqrt{\left(4\ -\ 3\right)^2\ +\ \left(7\ -\ 1\right)2}$$

• $$d\ =\ \sqrt{\left(7\ -\ 3\right)^2\ +\ \left(1\ -\ 4\right)^2}$$

• $$d\ =\ \sqrt{\left(7\ -\ 4\right)^2\ +\ \left(1\ -\ 3\right)^2}$$

• $$d\ =\ \sqrt{\left(3\ -\ 7\right)^2\ +\ \left(4\ -\ 1\right)^2}$$

• $$d\ =\ \sqrt{\left(3\ +\ 7\right)^2\ -\ \left(4\ +\ 1\right)^2}$$

Multiple Choice

Find the length of the missing side. #10

• 48 in.

• 52 in.

• 16 in.

• 24 in.

Multiple Choice

Find the length of the missing side. #1

• 17 cm

• 22 cm

• 15 cm

• 13 cm

Using the Pythagorean theorem to find the distance

Multiple Choice

Find the distance between (0, 10) and (12, 1).

• 12

• 11

• 15

• 16

Multiple Choice

Find the distance between the points (5, 7) and (-2, -2).

• 5.7

• 5.8

• 8.6

• 11.4

Multiple Choice

Find the distance between these two points.

• 13

• 7.9

• 9.2

• 3.6

The Midpoint Formula

Average of your x coordinates, Average of your y coordinates

Midpoint Formula

Discovering the formula & practice

Find the midpoint of the points (-3,3) & (5,3).

To find the midpoint,

1. Plug in (-3) for X₁ and plug in (3) for Y₁.

2. Plug in (5) for X₂ and plug in (3) for Y₂.

3. Simplify your answer to find the coordinate that lies between the two points.

Multiple Choice

What is the midpoint between (3,-1) and (7,-5)?

• (5,-2)

• (5,-3)

• (10,-6)

• (2,-2)