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Question

Find the area of the triangle formed by joining the midpoints of the sides of the triangle with coordinates A (-4, 3), B (2, 3) and C (4, 5).


A

2

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B

0.5

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C

1

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D

1.5

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Solution

The correct option is D

1.5


The mid points of AB, BC and CA are ( 4+22, 3+32), ( 4+22, 3+52) and ( 4+42, 5+32) respectively and lets denote them as D, E and F. So D(-1, 3), E(3, 4) and F(0, 4).

Suppose x1 = -1, y1 = 3

x2 = 3, y2 = 4

x3 = 0, y3 = 4

Area of a triangle = 12[ x1(y2 - y3) + x2( y3 - y1) + x3(y1 - y2)]

= 12[ -1(4 - 4) + 3(4 - 3) + 0(3 - 4)]

= 1.5 sq units


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