# doesn't look lyk it...but it is..

this question is from co-ordinate geometry...
if the straight lines y=4-3x ; ay=x+10 ; 2y+bx+9=0 represent the three consecutive sides of a rectangle then what is the value of ab?
plz show the work out as well

• Astha Gupta ·

i started this way...
the first and the third lines are the same since the opposite sides of the rectangle are equal. therefore their slopes are also the same.
slope of the first line,
y=4-3x (written in the form of y=mx+c)
i.e. -3............(1)
now,the equation of line 3 can be written as,
2y+bx+9=0
→2y= -bx-9
→y= -bx-92
→y=-b2x-92(written in the form of y=mx+c)
therefore the slope of the line is -b2.........(2)
equating (1) and (2)...
-3=-b/2
→b=6
i hope this was the right way to get the value of b...but how to get the value of a afterwards...???

• Astha Gupta ·

oh...something strike me...plzz..check if its wrong
in the equation of the second line, the slope is.
ay=x+10
→y=x+10/a
→y=1ax+10a
i.e. slope=1/a
now, the first line and the second line are perpendicular to each other. therefore product of their slopes is -1
i.e. -3 x 1a=-1
→a=3
hence the value of ab is = 3*6=18

• Manish Shankar ·

Yes good work Astha :)

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