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JAMB Mathematics 2019 Paper

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Question : 22

Total: 73

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.

m = 0, n = 4
m = 4, n = 0
m = 2, n = 2
m = -2, n = 4

Solution:

Concept:

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

Explanation:

For points

Q(m, n)

and

R(n, -4)

, the midpoint is:

\left( \frac{m+n}{2}, \frac{n-4}{2} \right)

This equals

P(2, m)

, so we equate coordinates.

Equating the

x

-coordinates:

\frac{m+n}{2} = 2

m + n = 4 \quad \dots (1)

Equating the

y

-coordinates:

\frac{n-4}{2} = m

n - 4 = 2m \quad \dots (2)

From (2),

n = 2m + 4

.

Substitute into (1):

m + 2m + 4 = 4

3m = 0

m = 0

Then

n = 2(0) + 4 = 4

.

Answer:

m = 0

and

n = 4

.

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