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Question

The co-ordinates of the vertices P, Q, R & S of square PQRS inscribed in the triangle ABC with vertices A ≡ (0, 0), B (3, 0) & C ≡  (2, 1) given that two of its vertices P, Q are on the side AB are respectively :

Options

A.
B.
C.(1, 0),
D.

Solution

    
Let co-ordinates of P are (x1, 0) and side of square is ′a′
∴  Q (x1 + a, 0)
S (x1 , a)
R (x1 + a, a)
Now,
   mAS = mAC
⇒  ⇒  x1 = 2a          ....(1)
mBR = mBC
⇒  = - 1    ⇒ x1 + 2a - 3 = 0      ...(2)
from (1) & (2) a =  & x1 =
co-ordinates of P, Q, R, & S can be determined.

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