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In the rectangular coordinate system above, if point R

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by M7MBA » Mon Apr 22, 2019 6:10 am

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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

[spoiler]OA=B[/spoiler]

Source: Official Guide.
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by [email protected] » Mon Apr 22, 2019 1:04 pm
Hi M7MBA,

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 Apr 23, 2019 7:01 pm
M7MBA 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

[spoiler]OA=B[/spoiler]

Source: Official Guide.
Notice that the y-coordinate of the point R will be the height of triangle ORP. We see that the base is 4; thus:

4 x h x 1/2 = 12

2h = 12

h = 6

So the y-coordinate of point R is 6.

Answer: B

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