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The area bounded by the curves |x + y| = 1 and |x - y| = 1

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by Vincen » Fri Sep 08, 2017 2:51 pm
The area bounded by the curves |x + y| = 1 and |x - y| = 1 is

A. 3
B. 4
C. 2
D. 1
E. None

The OA is C.

Can I do this exercise without making the graph of the curves? I mean, only with the equations?
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by Jay@ManhattanReview » Sat Sep 09, 2017 12:14 am
Vincen wrote:The area bounded by the curves |x + y| = 1 and |x - y| = 1 is

A. 3
B. 4
C. 2
D. 1
E. None

The OA is C.

Can I do this exercise without making the graph of the curves? I mean, only with the equations?
Well, I would not suggest that you go for equation method. It will take more time, though it can be done. With the help of the equations you will find the coordinates of 4 points and then you will have to calculate the distances between the points to find out the length of the area.

Plotting the lines on a coordinate plane is easier than you think.

We have |x + y| = 1. This gives two straight lines: x + y = 1 and x + y = -1

We also have |x - y| = 1. This gives two straight lines: x - y = 1 and x - y = -1

Once you plot these 4 straight lines, you can find the length of diagonals and then the sides of the square, thereby area of the square = 2.

The correct answer: C

Hope this helps!

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