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QOTD#10 Points A and B are shown in the xy-plane above.

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QOTD#10 Points A and B are shown in the xy-plane above. [#permalink] New post 12 Sep 2016, 11:37
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Question Stats:

66% (01:20) correct 33% (00:48) wrong based on 36 sessions
Attachment:
#GRepracticequestion Points A and B are shown in the xy-plane above.jpg
#GRepracticequestion Points A and B are shown in the xy-plane above.jpg [ 15.19 KiB | Viewed 1334 times ]


Points A and B are shown in the xy-plane above. Point C (not shown) is above the x-axis so that the area of triangle ABC is 10. Which of the following could be the coordinates of C?

Indicate all such coordinates.

A. (0, 4)
B. (1, 3)
C. (2, 5)
D. (3, 4)
E. (4, 5)


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Question: 18
Page: 207
[Reveal] Spoiler: OA

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Re: QOTD#10 Points A and B are shown in the xy-plane above. [#permalink] New post 12 Jun 2019, 10:58
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Explanation

Notice that the length of the triangle's base here is FIXED at 5 units
Attachment:
Points A and B are shown in the xy-plane above.1.png
Points A and B are shown in the xy-plane above.1.png [ 47.86 KiB | Viewed 736 times ]

At this point, we need only determine the triangle's HEIGHT

Area of triangle = (base)(height)/2
We're told that the triangle's area is 10.
Since the base has length 5, we can write: (5)(height)/2 = 10
Solve: height = 4

So, as long as the height of the triangles is 4 units, the triangle's area will be 10
For example, this triangle has a height of 4, so its area will be 10:
Attachment:
Points A and B are shown in the xy-plane above.2.png
Points A and B are shown in the xy-plane above.2.png [ 49.2 KiB | Viewed 736 times ]



And this triangle also has a height of 4, so its area will be 10:
Attachment:
Points A and B are shown in the xy-plane above.3.png
Points A and B are shown in the xy-plane above.3.png [ 49.7 KiB | Viewed 734 times ]


So, ANY point with y-coordinate 4 will create a triangle with area 4.

Check the answer choices for those with y-coordinate 4...

Answer: A & D

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Re: QOTD#10 Points A and B are shown in the xy-plane above.   [#permalink] 12 Jun 2019, 10:58
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QOTD#10 Points A and B are shown in the xy-plane above.

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