Question

What is the area of a triangle with vertices (1,0) (5,0) (3,4)

Answer 1

The area of the triangle is of 8 units of area.

Explanation:

Answer:

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 (1,0) (5,0) (3,4). So

`A = \pm 0.5 \left|\begin{array}{ccc}1&0&1\\5&0&1\\3&4&1\end{array}\right|`

`A = \pm 0.5(1*0*1+0*1*3+1*5*4-1*0*3-0*5*1-1*1*4)`

`A = \pm 0.5*(20-4)`

`A = \pm 0.5*16 = 8`

The area of the triangle is of 8 units of area.