The coordinates 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?

1 Answer
CW
Jan 8, 2018

see explanation.

Explanation:

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Given #PQRS# is a square, #=> PQ=QR=RS=SP#,
#(SP)/(AP)=1/2, => AP=2SP=2PQ#
#(QR)/(QB)=1/1, => QR=QB=PQ#
As #AP+PQ+QB=AB=3#,
#=> 2PQ+PQ+PQ=3#,
#=> 4PQ=3, => color(red)(PQ=3/4), => QR=RS=SP=3/4#
Hence, #P=(AP,0)=(2xx3/4,0)=(3/2,0)#
#Q=(AP+PQ,0)=(3/2+3/4,0)=(9/4,0)#,
#R=(9/4,3/4)#
#S=(3/2,3/4)#

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