Question

Use the figure to the right to find the value of PT. T is the midpoint of PQ.

PT = 3x + 3 and TQ = 5x - 9

Answer 1

`PQ = 42`

Explanation:

Given

`PT = 3x + 3`

`TQ = 5x - 9`

Midpoint, T

Required

Determine PT

First, the value of x has to be calculated;

Since T is the midpoint, then:

`PT = TQ`

This implies

`3x + 3 = 5x - 9`

Solve for x

`3x - 5x = -3 - 9`

`-2x = -12`

`x = -12/-2`

`x = 6`

Length PQ can then be calculated using:

`PQ = PT + TQ`

`PQ = 3x +3 + 5x -9`

Collect Like Terms

`PQ = 3x+ 5x +3 -9`

`PQ = 8x -6`

Substitute 6 for x

`PQ = 8 * 6 - 6`

`PQ = 48 - 6`

`PQ = 42`