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Question

For an equilateral triangle, one side lies on x+y=6 and the 3rd vertex is mirror image of the origin in the mirror x+y=6. Then the coordinates of other two vertices are


Correct Answer
A
(3+3,33)
Your Answer
B
(3+3,3+3)
Correct Answer
C
(33,3+3)
Your Answer
D
(33,33)

Solution

The correct options are
A (3+3,33)
C (33,3+3)
​​​​Let P(x,y) be the image of origin about x+y=6


The line perpendicular to x+y=6 and passes through (0,0) will be y=x
So, intersection of x=y and x+y=6 will give the midpoint of QR i.e., T
T(3,3)
Now, OT=TP=32 
QRsin60=32    (RP=QR=PQ)
QR=26
Now, x+y=6
So any point on the line will be 
(3±rcos135°,3±rsin135°)=(3r2,3±r2)
where r=TQ=6
So, from the above condition 
x=33 and y=3±3

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