Question

5E. Given ▲ABC with vertices A(2, -1), B(5, 6), and C(-1, 4) as shown. Find the number of square units in the area of ▲ABC in the simplest form.

Answer 1

Area = 18 square units

Explanation:

Given

`A =(2,-1)` ---
`(x_1,y_1)`

`B =(5,6)` ---
`(x_2,y_2)`

`C = (-1,4)` ---
`(x_3,y_3)`

Required

The area of the triangle

This is calculated as:

`Area = (1)/(2)|x_1(y_2 - y_3) + x_2(y_3 - y_1) +x_3(y_1 - y_2)|`

`Area = (1)/(2) * |2(6 - 4) + 5(4 - -1) -1(-1 -6)|`

`Area = (1)/(2) * |2*2 + 5*5 -1*-7|`

`Area = (1)/(2) * |36|`

`Area = (1)/(2) * 36`

Area = 18 square units