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

Question

Find the area of the triangle whose vertices are: (i) (2, 3), (&#x2013;1, 0), (2, &#x2013; 4) (ii) (&#x2013;5, &#x2013;1), (3, &#x2013;5), (5, 2)

Philoid · Accepted Answer

Area of the triangle = [x₁ (y₂ – y₃) + x₂ (y₃ – y₁) + x₃ (y₁ – y₂)

(i) Area of the triangle = [2 (0+ 4) - 1 (-4 – 3) + 2 (3 – 0)

= (8 + 7 + 6)

= Square units

(ii) Area of the triangle = [-5 (-5 – 2) + 3 (2+ 1) + 5 (-1+ 5)

= (35 + 9 + 20)

= 32 square units