Question

What is the area of a triangle with vertices at (0, −2) , ​ (8, −2) ​ , and ​ (9, 1) ​ ? Enter your answer in the box

Answer 1

The area of a triangle is A=1/2*b*h

When we graph the vertices of the triangle on a graph, we see that the lowest points are at y=-2, and the highest point is at y=1. Therefore, our height is 3.
The base of the triangle goes from (0,-2) to (8,-2), which gives us a length of 8 for our base.

A=1/2*(8)*(3)
A=12

Answer 2

12 square unit.

Explanation:

Since, the area of a triangle having vertices
`(x_1, y_1)`,
`(x_2, y_2)` and
`(x_3, y_3)` is,

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

Here, the vertices of the triangle are (0, −2), ​(8, −2) and ​ (9, 1),

Hence, area of the given triangle is,

`A=(1)/(2)|0(-2-1)+8(1+2)+9(-2+2)|`

`=(1)/(2)| 0+24+0|`

`=(24)/(2)`

`=12\text{ square unit}`