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Question

Prove that the points (4,1),(2,4),(4,0) and (2,3) are the vertices of a rectangle.

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Solution

hit A(4,1), B(2,4), C(4,0) and D(2,3) be the given points (circles)

Now, AD=(2+4)2+(3+1)2

=52

BC=(4+2)2+(0+4)2

=52

AB=(2+4)2+(4+1)2

=4+9

=13

CD=(24)2+(30)2

=13

AD=BC and AB=CD

Hence ABCD is a parallelogram

Now, AC=(4+4)2+(0+1)2

=65

BD=(2+2)2+(3+4)2=65

Clearly AC2=65=AB2+BC2

=(52)2+(13)2=65

and (BD)2=BC2+CD2

65=52+13=65

Hence, ABCD is a rectangle

The points (4,1, )(4,0) and (2,3) are which of rectangle.

1433670_973727_ans_7acf39b59ba24b258d064e85f640a37c.png

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