Lester wrote:
In the xy-plane, the graphs of x=3 and y = 6 intersect at point P, and the graphs of x=3 and y=-2 intersect at point Q. Origin O, point P, and point Q form a triangular region OPQ. what is the area OPQ?
(A)4
(B)8
(C)12
(D)16
(E)20
The first two lines, x = 3 and y = 6, intersect at the point (3, 6). So, point P is (3, 6).
The other two lines, x = 3 and y = -2, intersect at the point (3, -2). So, point Q is (3, -2).
Now let's examine the triangle created by the points (3, 6), (3, -2) and (0, 0)
If we let the BASE of the triangle be the side with endpoints (3, 6) and (3, -2), then the length of the base = 6 - (-2) =
8This means the HEIGHT of the triangle must be
3, since the origin (0, 0) is a distance of 3 units away from the side with endpoints (3, 6) and (3, -2).
Area of triangle = (1/2)(base)(height)
= (1/2)(
8)(
3)
= 12
Answer: C