The coordinate of P, Q and R are (2, m), (-3, 1) and (6, n) respectively. If the length of PQ is 5sqrt(2) units and midpoint of QR is ((3)/(2), -1) find the possible value of m and n.

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1. MATHEMATICS

a) The coordinate of P, Q and R are $(2, m)$, $(-3, 1)$ and $(6, n)$ respectively. If the length of PQ is $5\sqrt{2}$ units and midpoint of QR is $(\frac{3}{2}, -1)$ find the possible value of $m$ and $n$.

Step 1: Use the distance formula for PQ.
The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.
Given $P(2, m