Title: How to find the Distance, Midpoint, and Slope between two points.
1How 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.
2Distance 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.
3The Distance Formula!
4Lets try an example! Find the distance between
points A(3, 5) and B(7, 8).
B(7, 8)
A(3, 5)
5x1, y1
x2, y2
A(3,5) and B(7,8)
First step is to substitute your variables in the
correct spot
Try putting x1, y1 and x2, y2 above your points
Remember the order of operations Simplify the
parenthesis first!!
Square the numbers before you add.
Make sure you take the square root!!
6Lets try another example! Find the distance
between points C(-2, 7) and D(4, 1).
C(-2, 7)
D(4, 1)
7x1, y1
x2, y2
C(-2, 7) and D(4, 1)
Remember to label above your points.
What do you do when you have to subtract a
negative?
Its like adding the positive.
If the square root is not a whole number, round
to at least 2 decimal places
8The Midpoint Formula!
9Lets try an example! Find the midpoint between
points A(3, 5) and B(7, 8).
B(7, 8)
Mid Pt(?, ?)
A(3, 5)
10x2, y2
x1, y1
A(3, 5) and B(7, 8)
Place the labels above the points.
Substitute variables in the correct places.
Add the numerators before dividing.
Remember to keep the answers separated by a comma
because they are x and y coordinates of a point.
11Lets try another example! Find the midpoint
between points C(-2, 7) and D(4, 1).
C(-2, 7)
Mid pt(?, ?)
D(4, 1)
12x2, y2
x1, y1
C(-2, 7) and D(4, 1)
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.
13The Slope Formula!
14Lets try an example! Find the slope between
points A(3, 5) and B(7, 8).
B(7, 8)
A(3, 5)
15x1, y1
x2, y2
A(3, 5) and B(7,8)
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.
16Lets try another example! Find the slope between
points C(-2, 7) and D(4, 1).
C(-2, 7)
D(4, 1)
17x1 , y1
x2, y2
C(-2, 7) and D(4,1)
Label!!!
Subtracting a negative is just like adding a
positive.
The fraction can be reduced if it becomes a whole
number.
18Follow-Up Questions
- Answer the following questions on loose leaf and
hand them in to your math teacher.
19Follow-Up Questions
Find the distance, midpoint and slope for the
following sets of points
- (2, 5) and (8, 3)
- (-4, 4) and (5, 7)
- (0, 9) and (6, 1)
- (7, -11) and (10, 4)
- (3, 3) and (8, 8)
- 6. (21, 16) and (14, 5)
- (2.4, 3.2) and (5.6, 1.7)
- (-10, 11.3) and (-3, 7)
- (34, -2) and (-12, -18)
- (-5.2, -8.5) and (-6.23, 5.7)