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JAMB Mathematics 2011 Paper

Question : 28

Total: 46

The midpoint of P(x, y) and Q(8, 6) is (5, 8). Find x and y.

Solution:

Concept:

The midpoint formula gives the average of the corresponding coordinates of two points.

Explanation:

Given points

P(x, y)

and

Q(8, 6)

, the midpoint is

\left(\frac{x+8}{2}, \frac{y+6}{2}\right)

This midpoint equals

(5, 8)

So,

\frac{x+8}{2} = 5

Multiply both sides by

2

x + 8 = 10

Thus,

x = 10 - 8 = 2

Also,

\frac{y+6}{2} = 8

Multiply both sides by

2

y + 6 = 16

Thus,

y = 16 - 6 = 10

Therefore,

P(2, 10)

Answer:

(2, 10)

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