Question

What is the area of a triangle with vertices (3,0) (9,0) (7,6)

Answer 1

The area of the triangle is of 21 units of area.

Explanation:

The area of a triangle with three vertices
`(x_1,y_1),(x_2,y_2),(x_3,y_3)` is given by the determinant of the following matrix:

`A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|`

In this question:

Vertices (3,0) (9,0) (7,6). So

`A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|`

`A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)`

`A = \pm 0.5*(63-21)`

`A = \pm 0.5*42 = 21`

The area of the triangle is of 21 units of area.