In the coordinate plane, three vertices of rectangle ABCD are A(0, 0), B(0, a), and D(b, 0). What are the coordinates of point C?

1 Answer
Shwetank Mauria
Feb 11, 2017

Coordinates of #C# are #(b,a)#

Explanation:

As #A(0,0)# and #B(0,a)# have abscissa as #0#, they fall on #y#-axis. Similarly #A(0,0)# and #D(b,0)# have ordinate as #0#, they fall on #x#-axis.

As such #BC#||#AD# i.e. parallel to #x# axis and as such #B# and #D# must have common ordinate i.e. #a#.

Also #CD#||#AB# i.e. parallel to #y# axis and as such #C# and #D# must have common abcissa i.e. #b#.
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Hence, coordinates of #C# are #(b,a)#

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