Find the area of the triangle whose vertices are:
(i) $(2, 3)$ , $(- 1, 0)$ , $(2, - 4)$
(ii) $(- 5, - 1)$ , $(3, - 5)$ , $(5, 2)$

(i) 32 sq. units

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(ii) 32 sq. units

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(ii) 10.5 sq. units

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(i) 10.5 sq. units

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Solution

The correct options are
A (ii) 32 sq. units
C (i) 10.5 sq. units
Area of a triangle with vertices $(x_{1}, y_{1})$ ; $(x_{2}, y_{2})$ and $(x_{3}, y_{3})$ is $∣ ∣ ∣ \frac{x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})}{2} ∣ ∣ ∣$

1. Area of triangle with vertices, $(2, 3), (1, 0), (2, 4) = ∣ ∣ ∣ \frac{2 (0 + 4) - 1 (- 4 - 3) + 2 (3 - 0)}{2} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{8 + 7 + 6}{2} ∣ ∣ ∣ = \frac{21}{2} s q u n i t s$

2.Area of triangle with vertices, $(- 5, - 1), (3, - 5), (5, 2) = ∣ ∣ ∣ \frac{- 5 (- 5 - 2) + 3 (2 + 1) + 5 (- 1 + 5)}{2} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{35 + 9 + 20}{2} ∣ ∣ ∣ = \frac{64}{2} = 32$ sq units

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Find the area of the triangle whose vertices are:(i)(2,3), (−1,0), (2,−4)(ii)(−5,−1), (3,−5), (5,2)

Find the area of the triangle whose vertices are:
(i) $(2, 3)$ , $(- 1, 0)$ , $(2, - 4)$
(ii) $(- 5, - 1)$ , $(3, - 5)$ , $(5, 2)$