If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find the values of m and n.

A.

m = 0, n = 4

B.

m = 4, n = 0

C.

m = 2, n = 2

D.

m = -2, n = 4

Correct answer is A

Q(m, n) and R(n, -4)

Midpoint : P(2, m)

\(\implies (\frac{m + n}{2}, \frac{n - 4}{2}) = (2, m)\)

\(m + n = 2 \times 2 \implies m + n = 4 ... (i)\)

\(n - 4 = 2 \times m \implies n - 4 = 2m ... (ii)\)

Solving (i) and (ii) simultaneously,

m = 0 and n = 4.