# Midpoint theorem examples

Example 1

Find the distance A to C

The lines B to C and B to A are bisected at their midpoints

x to y must therefore be parallel to A to C

And midpoint theorem tells us that

x to y is 1/2 A to C

Therefore

A to C=2times6

A to C=12

Example 2

Find the distance AB

The lines xy and xz are bisected at their midpoints

Therefore A to B and y to z must be parallel

And midpoint theorem tells us that

A to B is 1/2yz

Therefore

A to B=5

Example 3

Find the distance x to y in the following diagram

Solution

Using Pythagoras theorem 8^2+6^2=H^2

Therefore

H^2=64+36

H^2=100

H=10

The lines A to C and C to B are bisected at their midpoints

x to y must therefore be parallel to A to B

And midpoints theorem tells us that

x to y is 1/2A to B

Therefore x to y is 1/2times 10

Answer: x to y=5