Jambmaths question:
The midpoint of P (x, y) and Q (8, 6) is (5, 8). Find x and y.
Option A:
(2,12)
Option B:
(2, 6)
Option C:
(2, 8)
Option D:
(2, 10)
Jamb Maths Solution:
$\begin{align} & \text{The midpoint of a line segment is given as} \\ & (x,y)=\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \\ & \therefore (5,8)=\left( \frac{{{x}_{1}}+8}{2},\frac{{{y}_{1}}+6}{2} \right) \\ & \frac{{{x}_{1}}+8}{2}=5,\text{ }\frac{{{y}_{1}}+6}{2}=8\text{ } \\ & {{x}_{1}}+8=10,\text{ }{{y}_{1}}+6=16 \\ & {{x}_{1}}=2,\text{ }{{y}_{1}}=10 \\ & (x,y)=(2,10) \\\end{align}$
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