Question

A triangle with vertices located at (−2, −2) and (4, −2) has an area of 24 square units. Which is one possible location of the other vertex? A) (4, 6) B) (4, 8) C) (6, −2) D) (−10, −2)

Answer 1

Answer: A) (4, 6)

Step-by-step explanation:

1. You can plot the given points (-2,-2) and (4,-2), as you can see in the first graph attached.

2. The formula for calculate the area of a triangle is:

$A=\frac{bh}{2}$

Where b is the base and h is the height.

3. As you can see in the first graph, the lenght of the base is:

$b=6units$

So, you must solve for the heigth:

$h=\frac{2A}{b}=\frac{2(24units^{2})}{6units}=8units$

3. Add 8 to the y-coordinate of both points given in the problem to know the coordinates of the other vertex:

(-2,-2+8)=(-2,6) (This is not an option)

(4,-2+8)=(4,6) (Option A. This is the answer).

4. Then, the triangle is shown in the second graph.