Question

What is the area of a triangle with verticals at(-4,1),(-7,5) and (0,1)

Answer 1

8

Explanation:

There are several ways of doing that, but probably the simplest one is to use the formula

`\bf Area=\left| (A_x(B_y-C_y)+B_x(A_y-C_y)+C_x(A_y-B_y))/(2)\right|`

where the vertices are

`\bf (A_x,A_y),(B_x,B_y),(C_x,C_y)`

and the bars | | means that you take the positive value of the number inside. For example | -3 | = 3.

Our vertices are

`\bf (A_x,A_y)=(-4,1)`

`\bf (B_x,B_y)=(-7,5)`

`\bf (C_x,C_y)=(0,1)`

Replace the values in the formula and we have

`\bf Area=\left| (-4(5-1)-7(1-1)+0(1-5))/(2)\right|=\left| (-4(4))/(2)\right|=\left| (-16)/(2)\right|=|-8|=8`