In the rectangular coordinate system, the vertices of a triangle have

Question

In the rectangular coordinate system, the vertices of a triangle have coordinates (-3,0), (3,2), and (0,11). What is the area of the triangle.

1.15
2.18
3.24
4.30
5.36

EMPOWERgmatRichC · Accepted Answer

Hi Turkish,

I'm going to offer some suggestions so that you can physically attempt this question on your own:

1) Draw a quick graph/sketch and plot those 3 co-ordinates. Connect the co-ordinates with lines. The graph doesn't have to be perfect.
2) Draw a rectangle "around" this triangle. Your rectangle should have the following 4 corners:
(-3,0), (3,0), (-3,11), (3,11)

3) You should see your original triangle and 3 right triangles. 
4) Figure out the area of the rectangle and subtract the areas of the 3 right triangles. This will give you the area of the original triangle.

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

hi turkish,
you can find the length of three sides..
1) \sqrt{( (-3-3)^2+(0-2)^2)} = \sqrt{40}  say side A
2) \sqrt{( (-3-0)^2+(0-11)^2)} = \sqrt{130}  say side B
3) \sqrt{( (3-0)^2+(2-11)^2)} = \sqrt{90} .. say side C

now you can see A^2 + c^2 = B^2... this means there is a right angle between sides A and C..
so area=1/2*A*C=1/2* \sqrt{40} * \sqrt{90} =30..
ans D...

fecob · Answer

Approximate by supposing that the vertex (3,2) is on the x-axis forming an isosceles triangle:
(3,2) -> (something>3;0)

Then, the area of this approximate isosceles triangle would be 6*11/2 = 33
The area of the actual triangle must be a little bit less than that of the approximate triangle. Thus 30, answer D.

stonecold · Answer

Here is an alternate and a bit easier approach provide you know how to solve a 3x3 matrix => USE THE DETERMINANT METHOD.
Area of a triangle => 1/2|Determinant Value|

Lets get the determinant of the matrix =>

1 -3 0
1 3 2
1 0 11

Determinant => 1(33) - (-3)(11-2) + 0(0-3) => 33+27=60

Hence the area of the triangle => 1/2 * 60 => 30

SMASH THAT D.

kannu44 · Answer

area of triangle = ½ |y₁ (x₂ - x₃) + y₂ (x₃ - x₁) + y₃ (x₁ - x₂)|
 =1/2 { 27 + 33} 
 =30

guptarahul · Answer

Using Matrix Method
|-3 0 1|
| 3 2 1|
| 0 11 1|

-3(2-11)+33=60
taking half of matrix=30

praveenmittal95605 · Answer

1/2 ( -3(2-11)+3(11-0)+0(0-2)) = 30

Paras96 · Answer

To find the area of a triangle given its coordinates, you can use the following formula:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

In this formula, (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices of the triangle.

For your triangle with coordinates (-3,0), (3,2), and (0,11), you can plug in the values into the formula:

x1 = -3, y1 = 0
x2 = 3, y2 = 2
x3 = 0, y3 = 11

Area = 1/2 * |-3(2 - 11) + 3(11 - 0) + 0(0 - 2)|

Now, calculate each part of the expression:

Area = 1/2 * |-3(-9) + 3(11) + 0|

Area = 1/2 * (27 + 33)

Area = 1/2 * 60

Area = 30 square units

So, the area of the triangle with coordinates (-3,0), (3,2), and (0,11) is 30 square units.

Hence D

egmat · Answer

When you're given coordinates of vertices, use the  Shoelace Formula  - it's the fastest and most reliable method!

Shoelace Formula: 
Area = 1⁄2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Given vertices: 
• A = ( -3 ,  0 )
• B = ( 3 ,  2 )
• C = ( 0 ,  11 )

Step-by-step:

Plug in the coordinates:
Area = 1⁄2 |( -3 )( 2  -  11 ) + ( 3 )( 11  -  0 ) + ( 0 )( 0  -  2 )|

Simplify inside the parentheses:
Area = 1⁄2 |( -3 )( -9 ) + ( 3 )( 11 ) +  0 |

Multiply:
Area = 1⁄2 | 27  +  33  +  0 |

Area = 1⁄2 ×  60  =  30

Answer: D

In the rectangular coordinate system, the vertices of a triangle have

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In the rectangular coordinate system, the vertices of a triangle have

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