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In the rectangular coordinate system above, if the area of right trian

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Bunuel
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In the rectangular coordinate system above, if the area of right trian [#permalink] New post   29 Dec 2015, 08:01
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In the rectangular coordinate system above, if the area of right triangle ABC is 24, what are the coordinates of point B?

A. (10, − 2)
B. (10, 2)
C. (8, − 2)
D. (2, 6)
E. It cannot be determined from the information given.

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Re: In the rectangular coordinate system above, if the area of right trian [#permalink] New post   29 Dec 2015, 08:45
Area(24) = 1/2(base*height)
Height AC= 6
Therefore base must be 8
For base to be 8 B must be (10,-2)
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Re: In the rectangular coordinate system above, if the area of right trian [#permalink] New post   29 Dec 2015, 21:49
Area of \(\triangle ABC = \frac{1}{2} * AC * CB\)

Distance AC = 6

Area of \(\triangle ABC\) = \(\frac{1}{2} * 6 * CB = 24\). Therefore CB = 8.

If CB = 8, Co-ordinate of B should be (10, -2)

Answer A
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Re: In the rectangular coordinate system above, if the area of right trian [#permalink] New post   30 Jun 2017, 14:24

In the rectangular coordinate system above, if the area of right triangle ABC is 24, what are the coordinates of point B?


\(Area = 24\)

\(Area = \frac{1}{2} * Base * Height\)

\(Area = \frac{1}{2} * AC * CB\)

\(24 = \frac{1}{2} * 6 * CB\)

\(24 = 3 * CB\)

\(CB = 8\)

For CB to be \(8\), x co-ordinate of Point B has to be \(10\) as \(x\) coordinate of point \(C = 2 = 10-2 = 8\)

Y co-ordinate of points C & B will remain same as \(-2\)

Hence the point \(B = (10, -2)\)

Hence, Answer is A
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Re: In the rectangular coordinate system above, if the area of right trian [#permalink] New post   19 May 2020, 04:05
Hello from the GMAT Club BumpBot!

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Re: In the rectangular coordinate system above, if the area of right trian [#permalink]
19 May 2020, 04:05
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