Question

1. find x if q is the mid - point of pr. pq = 19, and pr = 8x + 14.

Explanation:

Step1: Recall mid - point property

If \(Q\) is the mid - point of \(\overline{PR}\), then \(PQ=\frac{1}{2}PR\).

Step2: Substitute given values

We know that \(PQ = 19\) and \(PR=8x + 14\). So, \(19=\frac{1}{2}(8x + 14)\).

Step3: Solve the equation

First, multiply both sides of the equation by 2 to get \(2\times19=8x + 14\), which simplifies to \(38=8x+14\). Then subtract 14 from both sides: \(38 - 14=8x\), so \(24 = 8x\). Finally, divide both sides by 8: \(x=\frac{24}{8}=3\).

Answer:

\(x = 3\)