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Question

# If the four vertices of a square taken in order are (0,0) (0,5), (x,y) and (5,0), then (x,y) is

A
(-5,-5)
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B
(5,-5)
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C
(5,5)
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D
(-5,5)
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Solution

## The correct option is C (5,5) AB=BC=CD=AD BC=CD ⇒(√(o−x)2+(5−y)2)2=(√(x−5)2+(y−0)2)2 ⇒x2+25+y2−10y=x2+25−10x+y2 ⇒−10y=−10x ∴y=x.....(1) AD=√(x2−x1)2+(y2−y1)2 AD=√(5−0)2+(0−0)2 AD=√52 AD=5 Thus, AB=BC=CD=AD=5 In ΔABC,∠B=900 By pythagoras theorem, AB2+BC2=AC2 52+52=AC2 AC2=25+25=50 Now, AC=√(x−0)2+(x−0)2 AC2=(x−0)2+(x−0)2 50=2(x)2 x2=25 x=5 Therefore, y=x=5. Thus, (x,y)=(5,5) So, option c is correct.

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