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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
((ox)2+(5y)2)2=((x5)2+(y0)2)2
x2+25+y210y=x2+2510x+y2
10y=10x
y=x.....(1)
AD=(x2x1)2+(y2y1)2
AD=(50)2+(00)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=(x0)2+(x0)2
AC2=(x0)2+(x0)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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