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Sub 505 (Easy)|   Coordinate Geometry|                           
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Bunuel
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In the rectangular coordinate system above, the area of triangle RST 07 Feb 2014, 05:53
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

87% (01:05) correct 13% (01:23) wrong based on 2003 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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B
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Bunuel
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In the rectangular coordinate system above, the area of triangle RST 07 Feb 2014, 05:53
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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

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.
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blueseas
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In the rectangular coordinate system above, the area of triangle RST 07 Feb 2014, 08:12
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Area of triangle = 1/2 base*height
base = c-1
height = y co-ordinate of S = b
therefore area =\(((c-1)b)/2\)

hence OA should be = B
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In the rectangular coordinate system above, the area of triangle RST 07 Feb 2014, 09:03
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IMO - B

base = c-1
y = b
therefore area =((c-1)b)/2
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In the rectangular coordinate system above, the area of triangle RST 07 Feb 2014, 13:14
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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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In the rectangular coordinate system above, the area of triangle RST 21 Jun 2016, 01:04
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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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In the rectangular coordinate system above, the area of triangle RST 10 Aug 2020, 19:01
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Bunuel

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.
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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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In the rectangular coordinate system above, the area of triangle RST 10 Aug 2020, 22:42
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hanvd1990
Bunuel

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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Where did I assume that the triangle is right?
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In the rectangular coordinate system above, the area of triangle RST 15 Aug 2020, 23:33
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Bunuel
hanvd1990
Bunuel

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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Thank you Bunuel, when I read your explanation again, I understand it now.
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In the rectangular coordinate system above, the area of triangle RST 05 Sep 2024, 01:49
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