Bunuel wrote:

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

I'll calculate this one using the area formula of the trapezoid.

ℓ

2: x=2 means the hieght of the trapezoid is equal to 2

ℓ

1: 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 ℓ

1&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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