Question

use the figure to the right to find the value of pt. t is the mid - point of pq. pt = 6x + 8 and tq = 9x - 7. pt = □ (simplify your answer.)

Explanation:

Step1: Set up the equation

Since T is the mid - point of $\overline{PQ}$, then $PT = TQ$. So, $6x + 8=9x - 7$.

Step2: Solve for x

Subtract $6x$ from both sides: $8 = 9x-6x - 7$. Simplify to get $8 = 3x - 7$. Then add 7 to both sides: $8 + 7=3x$, so $15 = 3x$. Divide both sides by 3, and we find $x = 5$.

Step3: Find the value of PT

Substitute $x = 5$ into the expression for PT. $PT=6x + 8$. So, $PT=6\times5 + 8=30 + 8=38$.

Answer:

38