Question

the point q is the mid - point of pr. find the location of p. location of p :

Explanation:

Step1: Recall mid - point formula

If \(Q\) is the mid - point of \(\overline{PR}\), and the coordinates of \(Q = x_Q\), \(R=x_R\), \(P = x_P\), then \(x_Q=\frac{x_P + x_R}{2}\).

Step2: Rearrange the formula to solve for \(x_P\)

We know \(x_Q = 14\) and \(x_R=5\). Rearranging \(x_Q=\frac{x_P + x_R}{2}\) gives \(2x_Q=x_P + x_R\), so \(x_P=2x_Q - x_R\).

Step3: Substitute the values

Substitute \(x_Q = 14\) and \(x_R = 5\) into the formula \(x_P=2x_Q - x_R\). Then \(x_P=2\times14−5\).
\[x_P = 28 - 5=23\]

Answer:

23