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JAMB Mathematics 2012 Paper

Question : 26

Total: 48

Solution:

Concept:

Find the point where the two lines meet, then use the distance formula between that point and

(4, 3)

Explanation:

The lines are

y = 2x + 4

and

y = 7 - x

At their intersection, the

y

-values are equal, so equate them:

7 - x = 2x + 4

Rearrange to solve for

x

7 - 4 = 2x + x

3 = 3x

x = 1

Substitute

x = 1

into

y = 7 - x

y = 7 - 1 = 6

So the intersection point is

(1, 6)

Now find the distance between

(4, 3)

and

(1, 6)

using:

D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

D = \sqrt{(1 - 4)^2 + (6 - 3)^2}

D = \sqrt{(-3)^2 + (3)^2}

D = \sqrt{9 + 9}

D = \sqrt{18}

D = 3\sqrt{2}

Answer:

3\sqrt{2}

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