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)

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=(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=(2A)/(b)=(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.