Question

t is the midpoint of pq. what are pt, tq, and pq? 6x - 7 5x + 1

Explanation:

Step1: Set up equation for mid - point

Since T is the mid - point of PQ, PT = TQ. So, $6x - 7=5x + 1$.

Step2: Solve for x

Subtract $5x$ from both sides: $6x-5x - 7=5x-5x + 1$, which gives $x-7 = 1$. Then add 7 to both sides: $x=1 + 7$, so $x = 8$.

Step3: Find PT

Substitute $x = 8$ into the expression for PT: $PT=6x - 7=6\times8-7=48 - 7=41$.

Step4: Find TQ

Since PT = TQ, $TQ = 41$.

Step5: Find PQ

$PQ=PT + TQ$, so $PQ=41+41 = 82$.

Answer:

$PT = 41$, $TQ = 41$, $PQ = 82$