Introduction to Distance and Midpoint 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.

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.

Find the midpoint of the points (-4,5) & (2,-3).

1. Plug in (-4) for X₁ and (5) for Y₁.

2. Plug in (2) for X₂ and (-3) for Y_2.

3. Simplify your answer to find the middle coordinate.

Reduce your answers to decimals.

Sometimes your answers may not simplify evenly. In this case, you can rewrite your answers as decimals so that you can see where the coordinates lie on the graph.

Multiple Choice

Find the midpoint of the segment with the following endpoints:

(-9, 2) & (-5, -6).

• (-7, -2)

• (2, -7)

• (-9, -5)

• (2, -6)

Multiple Choice

Find the midpoint of the segment with the following endpoints:

(9, 8) & (3, 2).

• (5, 6)

• (9, 2)

• (6, 5)

• (3, 8)

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.

Find the distance between the points (-3,2) and (3,5).

1. Plug in (3) for X₂ and (-3) for X₁.

2. Plug in (5) for Y₂ and (2) for Y₁.

3. Simplify your answer to find d.

Note: Sometimes you will have to split your square roots to find a simpler answer.

Multiple Choice

Find the distance between the following points:

(1,4) & (4,0)

• 10

• 5

• 25

• 30

Multiple Choice

Find the distance between the two points:

(-3,-1) & (-2,4).

• $$\sqrt{2}$$

• 3

• $$\sqrt{10}$$

• $$\sqrt{26}$$

Multiple Choice

Find the distance between the two points:

(-3,-1) & (-2,4).

• $$\sqrt{2}$$

• 3

• $$\sqrt{10}$$

• $$\sqrt{26}$$

Multiple Choice

If you were to plot the point (4, -12) what would be the correct method?

• Up 4, left 12
• Right 4, up 12
• Down 4, left 12
• Right 4, down 12

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 )

Multiple Choice

What is the ordered pair for the hat?

• (-1,-3)
• (3,1)
• (-3,-1) 
• (1,3) 

Multiple Choice

Give the coordinates for POINT I.

• (-2, 5)
• (-2, -5)
• (2, 5)
• (2, -5)

Dropdown

To find the halfway point of a segment, use the ​

Select answer

To find the length of a segment, use the ​

Select answer

​

Select answer

is the midpoint formula

​

Select answer

is the distance formula

Finding an endpoint

• Use the midpoint formula.

• Substitute in values and solve for the variable.

​Let's do the next question together

Multiple Choice

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(5, -6) and M(4,3).

• (3, 12)

• (6, 4)

• (1, 2)

Multiple Choice

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(-3, 7) and M(-2,5).

• (6, 8)

• (-1, 3)

• (2, -4)

Multiple Choice

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(-2, 9) and M(8, 0).

• (-6, 0)

• ( 6, 9)

• (18, -9)

Multiple Choice

What formula is the distance formula?

Multiple Choice

Find the coordinate of the other endpoint given... Endpoint: (4, 1) Midpoint (7, 5)

• (8, 4)

• (-10,-9)

• (4,3)

• (10,9)

Multiple Choice

Find the coordinate of the other endpoint given... Endpoint (1, 2) Midpoint (7, -2)

• (4, 13)

• (13, -6)

• (13, -4)

• (10, 4)

Multiple Choice

Find the coordinates of the other endpoint given... Endpoint: (-1, 4) Midpoint: (-3, 0)

• (-6, 0)

• (-3, -2)

• (-5, -4)

• (-5, -2)

Fill in the Blanks

Find the coordinate of the other endpoint given... Endpoint (0, 9) Midpoint (8, 2)

Fill in the Blanks

Find the coordinate of the other endpoint given... Endpoint: (4, 3) Midpoint: (7, -2)