Question

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

Answer 1

Answer:

$PQ = 42$

Step-by-step 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

$PQ = 8 * 6 - 6$

$PQ = 48 - 6$

$PQ = 42$