Midpoint and distance

Midpoint and Distance Formulas

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.

Multiple Choice

Which calculation would determine the coordinates of the midpoint of the segment that connects

$$\left(-2,7\right)$$   and   $$\left(6,-5\right)$$  

• $$\left(\frac{-2+6}{2},\frac{7+-5}{2}\right)$$  

• $$\left(\frac{-2+7}{2},\frac{6+-5}{2}\right)$$  

• $$\left(\frac{-2+-5}{2},\frac{7+6}{2}\right)$$  

• $$\left(-2+6,7+-5\right)$$  

Multiple Choice

Complete the question to determine the coordinates of the midpoint of the segment that connects

$$\left(-2,7\right)$$   and   $$\left(6,-5\right)$$  

• $$\left(2,1\right)$$  

• $$\left(\frac{5}{2},\frac{1}{2}\right)$$  

• $$\left(-\frac{7}{2},\frac{13}{2}\right)$$  

• $$\left(4,2\right)$$  

Multiple Choice

What formula is the midpoint formula?

Multiple Choice

The endpoints of segment CD are C (3, -5) and D (7, 9). Find the coordinates of the midpoint?

• (3, 5)

• (5, 2)

• (6,8)

Multiple Choice

Find the midpoint of the segment with the following endpoints:

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

• (-7, -2)

• (2, -7)

• (-9, -5)

• (2, -6)

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?

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

What is the distance between the two points?

• $$2\sqrt{10}$$

• 4

• $$4\sqrt{10}$$

• $$10\sqrt{2}$$

Multiple Select

The Endpoints of RN are R(0,4) and N(-2,-3). Find the Distance

Choose 2

•   $$\sqrt[]{8}$$  

• 7.28

• $$\sqrt[]{53}$$   

• 2.83

Multiple Choice

Find the distance between (3, 24) and (7, 56).

• 32.1
• 32.2
• 32.3
• 32.4