How to find the Distance, Midpoint, and Slope between two points.

Please view this tutorial and answer the follow up questions on paper and

turn in to your teacher.

Distance = The length of a straight line between two points.

Midpoint = The point that is halfway between two endpoints on a line segment.

Slope = The rate of change of a line.

The Distance Formula!

D = (x2 −x1)2 + (y2 −y1)

2

Let’s try an example! Find the distance between points A(3, 5) and B(7, 8).

A(3, 5)

B(7, 8)

A(3,5) and B(7,8)

D = (x2 −x1)2 + (y2 −y1)

2

D = (7 −3)2 + (8 −5)2

D = (4)2 + (3)2

D = (16 + 9)

D = (25)

D =5

First step is to substitute your variables in the correct spot

Try putting x1, y1 and x2, y2 above your points

x1, y1 x2, y2

Remember the order of operations… Simplify the parenthesis first!!

Make sure you take the square root!!

Square the numbers before you add.

Let’s try another example! Find the distance between points C(-2, 7) and D(4, 1).

C(-2, 7)

D(4, 1)

C(-2, 7) and D(4, 1)

D = (x2 −x1)2 + (y2 −y1)

2

D = (4 −(−2))2 + (1−7)2

D = (6)2 + (−6)2

D = (36 + 36)

D = (72)

D ≈8.49

Remember to label above your points.

x1, y1 x2, y2

What do you do when you have to subtract a negative?

It’s like adding the positive.

If the square root is not a whole number, round to at least 2 decimal places

The Midpoint Formula!

Let’s try an example! Find the midpoint between points A(3, 5) and B(7, 8).

A(3, 5)

B(7, 8)

Mid Pt(?, ?)

A(3, 5) and B(7, 8)

M =(3+ 7)

2,(5 + 8)

2⎛⎝⎜

⎞⎠⎟

M =(10)2

,(13)2

⎛⎝⎜

⎞⎠⎟

M = 5,6.5( )

x1, y1x2, y2

Substitute variables in the correct places.

Place the labelsabove the points.

Add the numerators before dividing.

Remember to keep the answers separated by a comma because they are x and y coordinates of a point.

Let’s try another example! Find the midpoint between points C(-2, 7) and D(4,

1).

C(-2, 7)

D(4, 1)

Mid pt(?, ?)

C(-2, 7) and D(4, 1)

M =(−2 + 4)

2,(7 +1)

2⎛⎝⎜

⎞⎠⎟

M =(2)2

,(8)2

⎛⎝⎜

⎞⎠⎟

M = 1,4( )

x1, y1x2, y2

Remember to label above the points. What do you do

when you have to add a negative?

When adding numbers with two different signs, subtract them.

The Slope Formula!

S =y2 −y1x2 −x1

Let’s try an example! Find the slope between points A(3, 5) and B(7, 8).

A(3, 5)

B(7, 8)

A(3, 5) and B(7,8)

S =(y2 −y1)(x2 −x1)

S =(8 −5)(7 −3)

S =34

x1, y1 x2, y2

Remember to label.

Remember to subtract on the top and bottom first.

You can leave the answer in fraction form to see the rise over run.

Let’s try another example! Find the slope between points C(-2, 7) and D(4, 1).

C(-2, 7)

D(4, 1)

C(-2, 7) and D(4,1)

S =(y2 −y1)(x2 −x1)

S =(1−7)

(4 −(−2))

S =−66

S =−1

x1 , y1 x2, y2

Label!!!

Subtracting a negative is just like adding a positive.

The fraction can be reduced if it becomes a whole number.

Follow-Up Questions

Answer the following questions on loose leaf and hand them in to your math

teacher.

Follow-Up QuestionsFind the distance, midpoint and slope for the following sets

of points:

1. (2, 5) and (8, 3)

2. (-4, 4) and (5, 7)

3. (0, 9) and (6, 1)

4. (7, -11) and (10, 4)

5. (3, 3) and (8, 8)

6. (21, 16) and (14, 5)

7.(2.4, 3.2) and (5.6, 1.7)

8.(-10, 11.3) and (-3, 7)

9.(34, -2) and (-12, -18)

10.(-5.2, -8.5) and (-6.23, 5.7)