Question

What is the area of a triangle with the verticals of (-3,1),(-6,5), and (1,1)?

Answer 1

We need to find the area of a triangle using its verticals:

First, consider the points (-3,1) and (1,1), where both have the same y-value equal to 1. The x range is -3 to 1, therefore, the length of the horizontal side of the triangle( the base) is (1-(-3))=4.

Now, the third point is (-6,5) and the y-value we already know is equal to 1. Therefore, the vertical side distance from the horizontal line to the third point is 1-(5) =4.

Hence, we got the base=b =4 and the height =h= 4.

We use the area formula for triangles:

$A=\frac{b\cdot h}{2}$

Replace these values:

$A=\frac{4\cdot4}{2}=\frac{16}{2}$$A=8$

So, the area is equal to 8.