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Given the three points below

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by BTGmoderatorDC » Tue Nov 14, 2017 6:53 pm
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
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by ErikaPrepScholar » Wed Nov 15, 2017 7:00 am
It's a good call to visualize or sketch out this problem.

Looking at the numbers, we can see that (-3,-3), (3,-3) are each 6 down and 3 left/right of (0,3). This means that we have an isosceles triangle, where (0,3) is the top point, (-3,-3) to (3,-3) is the base and (-3,-3) to (0,3) and (3,-3) to (0,3) are the two equal sides. This means that if we were to draw a line from the top point (0,3) to the midpoint of the base (0,-3), we would have our height.

Base = (-3,-3) to (3,-3) = 6
Height = (0,3) to (0,-3) = 6

Then using the area formula:

(1/2) b*h = (1/2)(6)(6) = 18
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by EconomistGMATTutor » Wed Nov 15, 2017 10:35 am
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.
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Given the three points below

by Brent@GMATPrepNow » Wed Nov 15, 2017 11:41 am
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:
Image

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

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

Cheers,.
Brent
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by BTGmoderatorDC » Wed Jan 10, 2018 9:06 pm
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:
Image

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

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

Cheers,.
Brent
Thanks a lot!
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by BTGmoderatorDC » Wed Jan 10, 2018 9:07 pm
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.
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