Midpoint and Distance Lesson

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)

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

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

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

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

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

Fill in the Blanks

What is the distance between A & B?

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.

Fill in the Blanks

Find the midpoint between the points on the graph. Write your answer as an ordered pair.

Multiple Choice

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

• (5,-2)

• (5,-3)

• (10,-6)

• (2,-2)