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Question

Two sides of a square lie on the lines x+y=1and x+y+2=0 What is the area?

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Solution

Clearly the length of the side of the square is equal to the distance between the parallel lines x+y1=0 ....(i) and x+y+2=0 .....(ii)

Putting x=0 in (i) we get y=1 So (0,1) is a point on line (i)

Now Distance between the parallel lines = length of the from (0,1) to x+y+2=0= |0+1+2|12+12=32

Thus the length of the side of the square is 32 and hence its area = (32)2=92units2

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