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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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.
Source: Myschool Past Questions Archive (Record #55019)