Problem Solving

Brent@GMATPrepNow wrote:

lheiannie07 wrote:Given the three points below, what is the area of the triangle formed by connecting them?

(0,3), (-3,-3), (3,-3)

(A) 4.5
(B) 9
(C) 18
(D) 36
(E) 72

Here's a sketch of the triangle:


From here, we can see that the base has length 6, and the height is 6


Area = (base)(height)/2
= (6)(6)/2
= 36/2
= 18
= C

Cheers,.
Brent

EconomistGMATTutor wrote:

lheiannie07 wrote:Given the three points below, what is the area of the triangle formed by connecting them?

(0,3), (-3,-3), (3,-3)

(A) 4.5
(B) 9
(C) 18
(D) 36
(E) 72

How to come up with the Best Option?

OA C

Hi lheiannie07,
Let's take a look at your question.

Three points (0,3), (-3,-3), (3,-3) are making a triangle at the coordinate plane.
(0, 3) will be the top vertex of the triangle and (-3, -3) and (3, -3) are the vertices at the base of the triangle.

We know that,
Area of triangle = (1/2)*(Base)*(Height)

It means we need to find the length of base and height to find the area of triangle.
The vertices of base are (-3, -3) and (3, -3).
y coordinate is the same for both points, it means it is a horizontal line starting from x = -3 to x = 3, which includes 6 units at horizontal line.
Therefore,
Base = 6

To find height we need to draw a line from the top vertex (0, 3) to the base of the triangle which is a horizontal line at y = -3.
So if we draw a vertical line for the height of the triangle, it will start from y = 3, to y = -3, which includes 6 units at y-axis.
Therefore,
Height = 6

Now,
Area of triangle = (1/2)*(Base)*(Height)
Area of triangle = (1/2)*(6)*(6)
Area of triangle = (3)*(6) = 18

Therefore, Option C is correct.
Hope it helps.
I am available if you'd like any follow up.