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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
A triangle in the xy-coordinate plane has vertices with coordinates (7
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10 May 2021, 21:38
10 May 2021, 21:38
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A triangle in the xy-coordinate plane has vertices with coordinates (7, 0), (0, 8), and (20, 10). What is the area of this triangle?
A. 72
B. 80
C. 87
D. 96
E. 100
A. 72
B. 80
C. 87
D. 96
E. 100
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Status:Founder & Quant Trainer
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Re: A triangle in the xy-coordinate plane has vertices with coordinates (7
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11 May 2021, 00:43
11 May 2021, 00:43
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GeminiHeat wrote:
A triangle in the xy-coordinate plane has vertices with coordinates (7, 0), (0, 8), and (20, 10). What is the area of this triangle?
A. 72
B. 80
C. 87
D. 96
E. 100
A. 72
B. 80
C. 87
D. 96
E. 100
Area of triangle = \(\frac{1}{2}|20(8 - 0) + 0(0 - 10) + 7(10 - 8)| = \frac{174}{2} = 87\)
Alternate Approach:
Draw lines CD and CE (as shown in the figure)
Area of triangle ABC = Area of rectangle ODCE - Area of triangle AOB - Area of triangle BDC - Area of triangle CEA
= \((20)(10) - \frac{1}{2}(7)(8) - \frac{1}{2}(13)(10) - \frac{1}{2}(20)(2)\)
= \(200 - 28 - 65 - 20\)
= \(87\)
Attachments
Area of triangle ABC.jpg [ 619.75 KiB | Viewed 1980 times ]
gmatclubot
Re: A triangle in the xy-coordinate plane has vertices with coordinates (7 [#permalink]
11 May 2021, 00:43
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