(i) (2, 3), (-1, 0), (2, -4)<br> (ii) (-5, -1), (3, -5), (5, 2)

Solution:

The formula for calculating the area of a triangle is = 1/2 × [x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

(i) Given here,

x₁ = 2, x₂ = -1, x₃ = 2, y₁ = 3, y₂ = 0 and y₃ = -4

If we substitute all of the values in the formula above, we get

The area of triangle = 1/2 [2 {0- (-4)} + (-1) {(-4) – (3)} + 2 (3 – 0)]

= 1/2 {8 + 7 + 6}

= 21/2

As a result, the triangles’ area is 21/2 square units.

(ii) Given here,

x₁ = -5, x₂ = 3, x₃ = 5, y₁ = -1, y₂ = -5 and y₃ = 2

The area of the triangle = 1/2 [-5 { (-5)- (2)} + 3(2-(-1)) + 5{-1 – (-5)}]

= 1/2{35 + 9 + 20} = 32

As a result, the triangles’ area is 32 square units.