Distance Formula and Midpoint Formula Lesson

​2.1 Distance and Midpoint on the Coordinate Plane

Coach Taylor's Honor's Geometry Class

• Used for RIGHT triangles only

• Can also be used to calculate the DISTANCE between TWO points on a graph​

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​Some text here about the topic of discussion.

Pythagorean Theorm

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Multiple Choice

Find the Distance between the two points using $$a^2+b^2=c^2$$  

Remember to get rid of a square, we use a square root $$c=\sqrt[]{a^2+b^2}$$  

• 17

• 15

• 22

• 13

Multiple Choice

Find the Distance between the two points using $$a^2+b^2=c^2$$  

Remember to get rid of a square, we use a square root $$c=\sqrt[]{a^2+b^2}$$  

• 25 cm

• 42 cm

• 52 cm

• 48 cm

​Distance Formula

Find the two points, (x₁​,y₁) and (x₂,y₂)

Some text here about the topic of discussion

Find the distance

Multiple Choice

What is $$\left(x_1,y_1\right)$$  on the graph from your notes?

Always go left to right when reading the graph

• (-5,3)

• (5,-3)

• (-2,-3)

• (2,-3)

Multiple Choice

What is $$\left(x_2,y_2\right)$$  on the graph from your notes?

Always go left to right when reading the graph

• (-5,3)

• (5,-3)

• (-2,-3)

• (2,-3)

Multiple Choice

Set up the problem in the distance formula

• $$d=\sqrt[]{\left(-2--5\right)^2+\left(-3-3\right)^2}$$  

• $$d=\sqrt[]{\left(-5--2\right)^2+\left(-3+3\right)^2}$$  

• $$d=\sqrt[]{\left(5+2\right)^2+\left(3+3\right)^2}$$  

• $$d=\sqrt[]{\left(-5-2\right)^2+\left(3-3\right)^2}$$  

Multiple Choice

What is the answer?

• 45

• $$\sqrt[]{45}$$  

• 5.5

• $$-\sqrt[]{45}$$  

Multiple Choice

Find AB given A (-4,1) and B (3,-1)

• $$\sqrt[]{53}$$  

• $$53$$  

• $$\sqrt[]{5}$$  

• 5

• Not Here

Multiple Choice

Find the distance between each pair of points.

(-6,-10)  and (-2,-10)

• $$d=6$$  

• $$d=4$$  

• $$d=15$$  

• $$d=12$$  

Multiple Choice

Find the distance.

• 7.1
• 7.8
• 8.7
• 8.9

Multiple Choice

Which of the following formulas is the distance formula?

• $$\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)$$

• $$\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$

• $$a^2+b^2=c^2$$

• $$\frac{y_2-y_1}{x_2-x_1}$$

​Midpoint Formula

Find the two points, (x₁​,y₁) and (x₂,y₂)

Some text here about the topic of discussion

​Some text here about the topic of discussion.

Find the Midpoint

Multiple Choice

What is $$\left(x_1,y_1\right)$$  on the graph from your notes?

Always go left to right when reading the graph

• (-5,3)

• (5,-3)

• (-2,-3)

• (2,-3)

Multiple Choice

What is $$\left(x_2,y_2\right)$$  on the graph from your notes?

Always go left to right when reading the graph

• (-5,3)

• (5,-3)

• (-2,-3)

• (2,-3)

Multiple Choice

Set up the problem in the Midpoint formula

• $$m=\left(\frac{-5+-2}{2},\frac{3-3}{2}\right)$$  

• $$m=\left(\frac{-5+2}{2},\frac{3+3}{2}\right)$$  

• $$m=\left(\frac{-5--2}{2},\frac{-3-3}{2}\right)$$  

• $$m=\left(\frac{-5-3}{2},\frac{3-2}{2}\right)$$  

Multiple Choice

What is the answer?

• $$\left(-\frac{7}{2},0\right)$$  

• $$\left(\frac{2}{7},0\right)$$  

• $$\left(-\frac{2}{7},0\right)$$  

• $$\left(0,-\frac{7}{2}\right)$$  

Multiple Choice

Find the midpoint of segment AB given A (-7,4) and B (3,-4)

• (-2,4)

• (-5,4)

• (-2,0)

• (-5,0)

Multiple Choice

Find the midpoint:

• $$\left(3,-1\right)$$

• $$\left(-1,3\right)$$

• $$\left(3,4\right)$$

• $$\left(4,3\right)$$

Multiple Choice

Find the midpoint: $$\left(2,-7\right),\left(10,1\right)$$  

• (-3,6)

• (6,-3)

• (4,4)

• none

Multiple Choice

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?