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Difficulty: Sub 505 Level,   Coordinate Geometry,                           
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
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IMO - B

base = c-1
y = b
therefore area =((c-1)b)/2
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
Area of a triangle is given by: (Base * Height)/2

Base is measured by length on the x-axis, thus, c-1. Height is measured by the vertical axis y, so, coordinate b from point S.
Hence, b(c-1)/2, which is (B).
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
Area of triangle = \(\frac{1}{2}\) * base * height
Base is (c-1) for given triangle
Height is b for given triangle
Area = \(\frac{1}{2}\) * b * (c-1)

Correct Answer - B
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
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

The area of a triangle is 1/2*(base)(height):

(base) = c - 1 (the difference between the x-coordinates of points T and R).

(height) = b (the "height", the y-coordinate, of point S).

Therefore, the area is 1/2*(base)(height) = 1/2*(c - 1)b.

Answer: B.


Hi Bunuel, may I ask how you know this triangle is a right triangle? The picture does not indicate that it is a right triangle and we cannot figure out from the coordinates of the vertices either? Please correct me if I am wrong. Thank you!
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
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hanvd1990 wrote:
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

The area of a triangle is 1/2*(base)(height):

(base) = c - 1 (the difference between the x-coordinates of points T and R).

(height) = b (the "height", the y-coordinate, of point S).

Therefore, the area is 1/2*(base)(height) = 1/2*(c - 1)b.

Answer: B.


Hi Bunuel, may I ask how you know this triangle is a right triangle? The picture does not indicate that it is a right triangle and we cannot figure out from the coordinates of the vertices either? Please correct me if I am wrong. Thank you!


Where did I assume that the triangle is right?
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
Bunuel wrote:
hanvd1990 wrote:
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

The area of a triangle is 1/2*(base)(height):

(base) = c - 1 (the difference between the x-coordinates of points T and R).

(height) = b (the "height", the y-coordinate, of point S).

Therefore, the area is 1/2*(base)(height) = 1/2*(c - 1)b.

Answer: B.


Hi Bunuel, may I ask how you know this triangle is a right triangle? The picture does not indicate that it is a right triangle and we cannot figure out from the coordinates of the vertices either? Please correct me if I am wrong. Thank you!


Where did I assume that the triangle is right?

Thank you Bunuel, when I read your explanation again, I understand it now.
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
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Re: In the rectangular coordinate system above, the area of triangle RST [#permalink]
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