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.
I am available if you'd like any follow up.