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In the rectangular coordinate system above, if point R (not

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In the rectangular coordinate system above, if point R (not [#permalink]

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27 Dec 2012, 05:18
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In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

(A) 3
(B) 6
(C) 9
(D) 12
(E) 24
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Re: In the rectangular coordinate system above, if point R (not [#permalink]

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27 Dec 2012, 05:22
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In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

(A) 3
(B) 6
(C) 9
(D) 12
(E) 24

We are told that point R is above zero on the y-axis, so its coordinates are (y,0):
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OPR2.png [ 6.1 KiB | Viewed 8908 times ]
The area of triangle OPR is 1/2*base*height=1/2*OP*OR=1/2*4*OR=12 --> OR=6.

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Re: In the rectangular coordinate system above, if point R (not [#permalink]

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30 Jul 2014, 17:15
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Re: In the rectangular coordinate system above, if point R (not [#permalink]

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12 Sep 2015, 00:08
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Re: In the rectangular coordinate system above, if point R (not [#permalink]

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13 Jul 2016, 06:43
Attachment:
OPR.png
In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

(A) 3
(B) 6
(C) 9
(D) 12
(E) 24

We are given that a triangle is created using the x- and y-axes of the coordinate plane. The vertices of the triangle fall at point P (4,0), the origin (0,0), and point R (0,y). We see that we do not know the y-coordinate of point R. We can sketch it, as follows:

Given that one vertex falls on point (4,0) and the other vertex on point (0,0), we see that our base is equal to 4.

We are also given that the area of the triangle is 12. Using the formula for the area of a triangle and substituting the known values, we obtain:

area = (base x height)/2

12 = (4 x height)/2

24 = 4 x height

6 = height

The information above tells us that the distance between the origin and point R (which is on the y-axis) is 6. Thus, the y-coordinate of point R is 6.

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Jeffrey Miller
Jeffrey Miller

Re: In the rectangular coordinate system above, if point R (not   [#permalink] 13 Jul 2016, 06:43
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