Midpoint Formula
How to find the midpoint of a line segment by using the midpoint formula: 2 formulas (number line, coordinate plane), 3 example, and their solutions.
Formula
Formula: on a Number Line
If the endpoints of AB are A(x1) and B(x2),
then the midpoint of AB is
the mean of the endpoints:
M([x1 + x2]/2).
Formula: on a Coordinate Plane
If the endpoints of AB are A(x1, y1) and B(x2, y2),
then the midpoint of AB is
M([x1 + x2]/2, [y1 + y2]/2).
Example 1
Example 1
Solution
Set the mipoint of AB M.
The endpoints of AB are
A(-1) and B(5).
Then the midpoint M is
[-1 + 5]/2.
-1 + 5 = 4
4/2 = 2
So 2 is the answer.
Example 2
Example 2
Solution
Set the mipoint of AB M.
The endpoints of AB are
A(-3, 1) and B(5, 4).
Then the midpoint M is
M([-3 + 5]/2, [1 + 4]/2).
-3 + 5 = 2
1 + 4 = 5
2/2 = 1
So M(1, 5/2).
Example 3
Example 3
Solution
Set the coordinates of point B
(p, q).
It says
point M is the midpoint of AB.
A(-4, 5)
B(p, q)
Then M([-4 + p]/2, [5 + q]/2).
M(0, 2)
So write = (0, 2).
So M([-4 + p]/2, [5 + q]/2) = (0, 2).
The x coordinates are the same.
So [-4 + p]/2 = 0.
Multiply 2 to both sides.
Move -4 to the right side.
Then p = 4.
The y coordinates are the same.
So [5 + q]/2 = 2.
Multiply 2 to both sides.
Move 5 to the right side.
Then q = -1.
B(p, q)
p = 4
q = -1
So B(4, -1).
So B(4, -1) is the answer.