Question

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

Answer 1

Answer:

8

Step-by-step explanation:

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

$\bf Area=\left| \frac{A_x(B_y-C_y)+B_x(A_y-C_y)+C_x(A_y-B_y)}{2}\right|$

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

$\bf Area=\left| \frac{-4(5-1)-7(1-1)+0(1-5)}{2}\right|=\left| \frac{-4(4)}{2}\right|=\left| \frac{-16}{2}\right|=|-8|=8$