Question 32

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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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