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Re: In the coordinate plane above, if the equation of ℓ1 is y = x − 3 and [#permalink]

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03 Jan 2016, 23:45

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.

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
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Re: In the coordinate plane above, if the equation of ℓ1 is y = x − 3 and [#permalink]

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11 Dec 2017, 09:52

Is my approach right to get the value of Y? as it is given that y = x − 3 and we know that Li intersect L2 at x = 2 then putting the value of x in above equation we can get the value of Y and that is -1...am i doing some mistake?
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Re: In the coordinate plane above, if the equation of ℓ1 is y = x − 3 and [#permalink]

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30 Dec 2017, 21:56

sananoor wrote:

Is my approach right to get the value of Y? as it is given that y = x − 3 and we know that Li intersect L2 at x = 2 then putting the value of x in above equation we can get the value of Y and that is -1...am i doing some mistake?

sananoor What your doing is perfectly correct. the co-ordinates in clockwise are (0,0) (2,0) (3,0) (2,-1) (0,-3)
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