1.3 Notes: Midpoint & Distance Formulas

Midpoint & Distance

We use the midpoint formula to find the point that lies between 2 points on a line.

We use the distance formula to find the distance between 2 points.

Review: Graphing in the coordinate plane

Multiple Choice

Where is point A located?

• ( 7 , 2 )
• ( 2 , 6 )
• ( - 2 , 7 )
• ( 2 , 7 )

Multiple Choice

Where is point E located?

• ( 2, 0 )
• ( 2 , 2 )
• ( 0 , 2 )
• ( 0 , 0 )

Fill in the Blanks

Fill in the Blanks

Midpoint

• To find the midpoint of 2 points, plug in your points into the given formula.

• Simplify your answer to get the coordinate that lies directly in the middle of the 2 points.

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)

Multiple Choice

What is the midpoint between (4,12) and (-6,14)?

• (-1,13)

• (13,-1)

• (13,1)

• (5,13)

Multiple Choice

Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)

• (-1, 13)
• (13, 1)
• (13, -1)
• (5, 13)

Distance Formula

• To find the distance between two points, plug in the x and y values into the formula given.

• Simplify your answer so that you can find the distance (d) between the two points.

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.

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

• 5.7

• 5.8

• 8.6

• 11.4

Multiple Choice

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

• 12

• 11

• 15

• 16

Multiple Choice

What is the distance between AB?

• 0

• 5

• 4