Calculate the area of a parallelogram bounded by y-axis, the line #x=3#,a line #y=2x+1# and a line parallel to that line passing through #(2,7)?

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Answer 1 · 2017-11-30T09:14:04

Area of parallelogram is #6# units.

The line parallel to #y=2x+1# will be of the form #y=2x+k#.

As it passes through #(2,7)#, we have #7=2xx2+k# i.e. #k=3#

and hence two parallel lines have equations #y=2x+1# and #y=2x+3#.

As the difference in #y#-intercepts is #2#,

the side of parallelogram along #y#-axis is #2#.

Further, two other parallel lines are #x=0# and #x=3# and hence

vertical distance between them is #3#

Hence area of parallelogram is #2xx3=6# units.

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