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# In the rectangular coordinate system above, the area of triangle RST

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In the rectangular coordinate system above, the area of triangle RST  [#permalink]

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12 Dec 2017, 10:23
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15% (low)

Question Stats:

69% (00:42) correct 31% (00:29) wrong based on 32 sessions

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In the rectangular coordinate system above, the area of triangle RST is

(A) bc/2
(B) b(c – 1)/2
(C) c(b – 1)/2
(D) a(c – 1)/2
(E) c(a – 1)/2

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2017-12-12_1003_001.png [ 8.64 KiB | Viewed 716 times ]

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In the rectangular coordinate system above, the area of triangle RST  [#permalink]

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12 Dec 2017, 14:02
Attachment:

2017-12-12_1003_001.png [ 9.94 KiB | Viewed 504 times ]

When a line segment is drawn from the point S, such that
it forms the height of the triangle, it will be the height of
the triangle.

The coordinate of point P, such that SP is the height is (a,0)

Hence, the height will be $$\sqrt{(a-a)^2 + (b-0)^2} = b$$

We can find the length of the base using formula $$\sqrt{(c-1)^2 + (0-0)^2} = c-1$$

Therefore, the area of the triangle is $$\frac{1}{2}$$ * Base * Height = $$\frac{1}{2} * b * (c-1) = \frac{b(c-1)}{2}$$ (Option B)

*genxer123 - Made the necessary change! Thanks for informing
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In the rectangular coordinate system above, the area of triangle RST  [#permalink]

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12 Dec 2017, 15:41
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Bunuel wrote:

In the rectangular coordinate system above, the area of triangle RST is

(A) bc/2
(B) b(c – 1)/2
(C) c(b – 1)/2
(D) a(c – 1)/2
(E) c(a – 1)/2

Attachment:
The attachment 2017-12-12_1003_001.png is no longer available

Attachment:

2017-12-12_1003_001ed.png [ 15.28 KiB | Viewed 527 times ]

Area of triangle = $$\frac{b*h}{2}$$

Find base by subtracting x-coordinate of vertex R from vertex T:
Length of RT = (c - 1)

Drop an altitude from S.
The point of intersection with the base (Q in diagram), because the altitude is perpendicular to the base, has the same x-coordinate as S.
Coordinates of point Q are (a, 0)
The height of the triangle is the difference between the y-coordinate of S and the y-coordinate of Q:
b - 0 = b

So the area is

$$\frac{(c - 1)*b}{2} = \frac{b(c - 1)}{2}$$

pushpitkc , I think you mixed up your coordinates for the height of the triangle.
Where you dropped the altitude, x is not 0. x is a.
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In the rectangular coordinate system above, the area of triangle RST &nbs [#permalink] 12 Dec 2017, 15:41
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