Question

What is the area of this triangle need homework help

Answer 1

To find the area of a triangle, we can do the product of any base and the height corresponding to this base and divide it by 2.

`A=(1)/(2)\cdot b\cdot h`

The base can be any side, but in this case it is easier to pick the left side, because we can calculate its length by the vertical distance of the points (x1, y1) and (x2, y2).

So, the base is:

`b=\left(y_2-y_1\right)`

For the height, since we picked the left side, the height will be the distance from the other vertex, (x3, y3), and the base.

Because the base is a vertical line, every part of it has the same x value, x1. So, the distance from the point (x3, y3) will be simply the horizontal distance betweein it and the point x1, so:

`h=\left(x_3-x_1\right)`

Putting altogether, we have:

`A=(1)/(2)\left(y_2-y_1\right)\left(x_3-x_1\right)`