The coordinates of the points A and B are respectively (–3, 2) and (2, 3). P and Q are points on the line joining A and B such that AP = PQ = QB. A square PQRS is constructed on PQ as one side, the coordinates of R can be
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(b, d)
P, Q divide AB in the ratio of 1:2 and 2:1 respectively and hence the coordinates of P and Q are
and 
⇒ P 
and Q 
and PQ = 
Let the coordinates of R be (x, y)
Then QR = PQ ⇒ 
+ 
= 
... (i)
and QR is perpendicular to PQ
⇒ 
= –1 = –1 ⇒ 
= –5 
... (ii)
From (i) and (ii), we get 26 
= 
,
x – 
= ± 
⇒ x = 0 or x = 
From (ii), when x = 0, y = 
and when x = 
, y = 1
So the required coordinates of R are 
or 
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