Question

points p, q, and r are collinear. point q is between p and r, pq = 3z + 4, pr = 13z - 10, and qr = 9z + 3. find pq.

Explanation:

Step1: Use collinear - point property

Since P, Q, R are collinear and Q is between P and R, we have $PQ + QR=PR$.
Substitute the given expressions: $(3z + 4)+(9z + 3)=13z - 10$.

Step2: Simplify the left - hand side

Combine like terms: $3z+9z + 4 + 3=12z+7$. So, $12z + 7=13z - 10$.

Step3: Solve for z

Subtract $12z$ from both sides: $12z+7-12z=13z - 10-12z$.
We get $7=z - 10$.
Then add 10 to both sides: $7 + 10=z-10 + 10$, so $z = 17$.

Step4: Find PQ

Substitute $z = 17$ into the expression for PQ: $PQ=3z + 4$.
$PQ=3\times17+4=51 + 4=55$.

Answer:

55