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03 Jan 2016, 13:28
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:08) correct
27%
(02:25)
wrong
based on 280
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In the coordinate plane above, if the equation of ℓ1 is y = x − 3 and the equation of ℓ2 is x = 2, then what is the area of the shaded region?
(A) 3
(B) 4
(C) \(3 \sqrt{2}\)
(D) 4.5
(E) 5
Attachment:
2016-01-04_0026.png [ 9.48 KiB | Viewed 6812 times ]
04 Jan 2016, 05:37
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Bunuel
I'll calculate this one using the area formula of the trapezoid.
ℓ2: x=2 means the hieght of the trapezoid is equal to 2
ℓ1: y=x-3, to calculate the base we can set x=0 so y=-3 (Base 1)
To calculate the 2nd base we must find the point of intersection of lines ℓ1&2 --> y=2-3=-1 (Base 2)
We have everything we need to calculate the area:\(\frac{(Base1+ Base2)*Height}{2}\) = \(\frac{(3+1)*2}{2}=4\)
Answer B
General Discussion
04 Jan 2016, 00:45
Kudos
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I see that the shaded region is composed of two parts: a top rectangle and a bottom triangle. The final area will be the sum of those two parts.
Top rectangle:
The left bound is x = 0, right bound x = 2.
The top bound is y = 0, with the bottom bound at where our lines intersect. We calculate the intersection to be y = -1.
X = [0, 2]
Y = [0, -1]
Area for the rectangle: absolute(2 * -1) = 2.
Bottom triangle:
Our length is the same as the rectangle from above, 2.
To find our triangle height, we need to find where line 1 intersects with the origin. y = x - 3 -> y = -3.
Our triangle height is 3 - 1 = 2.
Our triangle area = (1/2) height*length -> (1/2) 2 * 2.
Area for the triangle = 2.
As I mentioned first in this post, our final area will be the area of the triangle + the area of the rectangle. Plugging in the calculated values from above, 2 + 2 = 4.
The answer should be B, 4.
Top rectangle:
The left bound is x = 0, right bound x = 2.
The top bound is y = 0, with the bottom bound at where our lines intersect. We calculate the intersection to be y = -1.
X = [0, 2]
Y = [0, -1]
Area for the rectangle: absolute(2 * -1) = 2.
Bottom triangle:
Our length is the same as the rectangle from above, 2.
To find our triangle height, we need to find where line 1 intersects with the origin. y = x - 3 -> y = -3.
Our triangle height is 3 - 1 = 2.
Our triangle area = (1/2) height*length -> (1/2) 2 * 2.
Area for the triangle = 2.
As I mentioned first in this post, our final area will be the area of the triangle + the area of the rectangle. Plugging in the calculated values from above, 2 + 2 = 4.
The answer should be B, 4.
