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On the xy-coordinate plane, point A lies on the y-axis and

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On the xy-coordinate plane, point A lies on the y-axis and  [#permalink]

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New post 06 Mar 2013, 11:13
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On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and an area of 30. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?

(A) (−6, −5)
(B) (−5, 12)
(C) (6, −9)
(D) (9, −8)
(E) (10, −3)

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Re: On the xy-coordinate plane, point A lies on the y-axis and  [#permalink]

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New post 06 Mar 2013, 11:39
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The area of the triangle so formed will be = 1/2 x base x height = 1/2 x |(X-coordinate of point C)| x |(Y-coordinate of point C)| = 30
=> |product of coordinates of point C| = 60

Choice B is the only option that leads to this, and is the answer.

Please note here that we need to use the modulus signs because we do not know if point A lies on the positive Y axis and if B lies on the positive X axis.
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Re: On the xy-coordinate plane, point A lies on the y-axis and  [#permalink]

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New post 06 Mar 2013, 11:53
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megafan wrote:
On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and an area of 30. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?

(A) (−6, −5)
(B) (−5, 12)
(C) (6, −9)
(D) (9, −8)
(E) (10, −3)


You could have B and A on either the positive/negative x and y axis respectively. So a total of 4 triangles are possible, which have a right angle at C. Now, for the rectangle OACB, where O is the origin, the area of the other triangle OAB will also be 30. Now the co-ordinate of B and A will be the (x,y) co-ordinates of C respectively. Thus, for B = (-5,0) and A = (0,12), we have the area of the triangle OAB as 30.

B.
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Re: On the xy-coordinate plane, point A lies on the y-axis and  [#permalink]

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New post 09 Mar 2013, 01:46
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okay.. the important thing to note is that AC is // to x-axis and BC is // to Y-axis.
and then we know the area is 30 so => the product of X coordinate of C and Y coordinate of C= 60
only answer choice that satisfies the same is (5,12) sign doesn't matter really!!
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Re: On the xy-coordinate plane, point A lies on the y-axis and  [#permalink]

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New post 22 Dec 2014, 01:30
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(5*12)/2=30

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Re: On the xy-coordinate plane, point A lies on the y-axis and  [#permalink]

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New post 09 Sep 2018, 00:57
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Re: On the xy-coordinate plane, point A lies on the y-axis and   [#permalink] 09 Sep 2018, 00:57
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