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In the rectangular coordinate (OG16)

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by [email protected] » Thu May 19, 2016 4:53 pm
Hi boomgoesthegmat,

From the diagram, we know that the base of triangle ORP = 4. We also know that it's area = 12, so we can combine those two pieces of information to find the height of the triangle (and by extension, the Y co-ordinate of point R).

Area = (1/2)(base)(height)

12 = (1/2)(4)(height)
12 = 2(height)
6 = height

Final Answer: B

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by Scott@TargetTestPrep » Tue Dec 12, 2017 6:32 am
boomgoesthegmat wrote:Image

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 point P lies at (4,0) and point R lies on the y-axis. Thus, we see that we have a right triangle with one vertex at point P, another at coordinate (0,0), and the other at point R. Thus, the base of the triangle is 4, and the height is the y-coordinate of point R.

Since we know the area of the triangle is 12, we can create the following equation in which y = the y-coordinate of point R.

area = (base x height)/2

12 = 4y/2

24 = 4y

6 = y

Answer: B

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by EconomistGMATTutor » Wed Dec 13, 2017 6:39 am
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
Hi boomgoesthegmat,
Let's take a look at your question.

The coordinates of P are (4, 0), therefore,
$$OP=4$$
Area of triangle ORP = 12

We know that:
Area of a triangle = (1/2) * (Base) * (Height)
$$Area=\frac{1}{2}\cdot OQ\cdot OP$$
$$12=\frac{1}{2}\cdot OQ\cdot4$$
$$12=OQ\cdot2$$
$$OQ=\frac{12}{2}$$
$$OQ=6$$

So the y-coordinate of Q is 6.
Therefore, Option B is correct.

Hope it helps.
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