Question

use the figure to the right to find the value of PT. T is the midpoint of line segment PQPT=3x+8 and TQ= 5x-6

Answer 1

We want to find the length of PT.

From the figure [given T is midpoint of PQ], we can write:

`PT+TQ=PQ`

We are given expressions for PT and TQ, we know they are equal. Thus, we can equate them and solve for x.

`\begin{gathered} PT=TQ \\ 3x+8=5x-6 \\ 8+6=5x-3x \\ 14=2x \\ x=(14)/(2) \\ x=7 \end{gathered}`

The length of PT is "3x + 8". We know x = 7, so we can figure out the length of PT:

`\begin{gathered} PT=3x+8 \\ PT=3(7)+8 \\ PT=21+8 \\ PT=29 \end{gathered}`