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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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Question Stats:
65% (02:51) correct
34% (03:34) wrong based on 29 sessions
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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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Re: A triangle in the xy-coordinate plane has vertices with coordinates (7
[#permalink]
11 May 2021, 00:43
11 May 2021, 00:43
2
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 2538 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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