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: m = 0, n = 4
Explanation
Q(m, n) and R(n, -4)
Midpoint : P(2, m)
⟹ (m+n/2,n − 4/2 )= (2,m)
m + n = 2 × 2 ⟹ m + n = 4...(i)
n − 4 = 2 × m ⟹ n − 4 =2m...(ii)
Solving (i) and (ii) simultaneously,
m = 0 and n = 4.
Q(m, n) and R(n, -4)
Midpoint : P(2, m)
⟹ (m+n/2,n − 4/2 )= (2,m)
m + n = 2 × 2 ⟹ m + n = 4...(i)
n − 4 = 2 × m ⟹ n − 4 =2m...(ii)
Solving (i) and (ii) simultaneously,
m = 0 and n = 4.