Jambmaths question:
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.
Option A:
m = 0, n = 4
Option B:
m = 4, n = 0
Option C:
m = 2, n = 2
Option D:
m = -2, n = 4
Jamb Maths Solution:
$\begin{align} & P(x,y)=P(2,m) \\ & Q({{x}_{1}},{{y}_{1}})=Q(m,n) \\ & R({{x}_{2}},{{y}_{2}})=R(n,-4) \\ & \text{Midpoint of a line segment }=(x,y)=\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \\ & (2,m)=\left( \frac{m+n}{2},\frac{n-4}{2} \right) \\ & 2=\frac{m+n}{2} \\ & m+n=4----(i) \\ & \frac{n-4}{2}=m \\ & 2m=n-4 \\ & 2m-n=-4---(ii) \\ & \text{adding (i) and (ii) together} \\ & 3m=0,\text{ }m=0 \\ & \text{Substitute }0\text{ for }m\text{ in }(i) \\ & 0+n=4 \\ & n=4 \\ & m=0,\text{ }=4 \\\end{align}$
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