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

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0.5

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1.5

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Solution

The correct option is D
1.5

The mid points of AB, BC and CA are $(\frac{- 4 + 2}{2}$ , $\frac{3 + 3}{2})$ , $(\frac{4 + 2}{2}$ , $\frac{3 + 5}{2})$ and $(\frac{- 4 + 4}{2}$ , $\frac{5 + 3}{2})$ respectively and lets denote them as D, E and F. So D(-1, 3), E(3, 4) and F(0, 4).

Suppose $x_{1}$ = -1, $y_{1}$ = 3

$x_{2}$ = 3, $y_{2}$ = 4

$x_{3}$ = 0, $y_{3}$ = 4

Area of a triangle $= \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]$

= $\frac{1}{2}$ [ -1(4 - 4) + 3(4 - 3) + 0(3 - 4)]

= 1.5

Area of a triangle = 1.5

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