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In the xy-plane, the graphs of x=3

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Lester
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In the xy-plane, the graphs of x=3 [#permalink] New post   10 Mar 2021, 05:09
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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
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C
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Re: In the xy-plane, the graphs of x=3 [#permalink] New post   22 Jun 2021, 15:22
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The question tells us that line x=3 intersects y=6 and y=-2 at points P and Q. Also these points with origin O are forming triangle.
Now to find the area of triangle we need to have the length of the base and height. "area of triangle = bh/2".

The base is PQ. Since P and Q have the same x-axis, the length of PQ is the difference of y values.
P=(3,6) and Q=(3,-2)
PQ length= 6-(-2)= 8

The height here is the distance from O "origin" to line x=3 or line PQ which is 3.

Area of triangle = (8*3)/2= 12.
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Re: In the xy-plane, the graphs of x=3 [#permalink] New post   10 Mar 2021, 05:49
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This is NOT a QCQ question :?

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Re: In the xy-plane, the graphs of x=3 [#permalink] New post   22 Jun 2021, 07:03
I believe the answer is 12.
am I correct? :?
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Re: In the xy-plane, the graphs of x=3 [#permalink] New post   22 Jun 2021, 07:45
Correct.

Added the OA. It would be great if you provide a detailed solution. The forum will be grateful.

GR3A wrote:
I believe the answer is 12.
am I correct? :?
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Re: In the xy-plane, the graphs of x=3 [#permalink] New post   11 Nov 2021, 12:28
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) = 8

This 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
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Re: In the xy-plane, the graphs of x=3 [#permalink]
11 Nov 2021, 12:28
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