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JAMB Mathematics 2013 Paper

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Question : 42

Total: 47

If the midpoint of the line PQ is (2,3) and the point P is (-2, 1), find the coordinate of the point Q.

(8,6)
(5,6)
(0,4)
(6,5)

Solution:

Concept:

The midpoint formula gives the average of the coordinates of two endpoints.

Explanation:

Let the coordinates of point

Q

be

(x, y)

.

The midpoint of

P(-2, 1)

and

Q(x, y)

is given by:

\left( \frac{-2 + x}{2}, \frac{1 + y}{2} \right)

This midpoint equals

(2, 3)

.

So, equate the

x

-coordinates:

\frac{-2 + x}{2} = 2

Multiply by

2

:

-2 + x = 4

Thus,

x = 6

.

Next, equate the

y

-coordinates:

\frac{1 + y}{2} = 3

Multiply by

2

:

1 + y = 6

Thus,

y = 5

.

Therefore,

Q = (6, 5)

.

Answer:

Q = (6, 5)

, which is option D.

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