The Total solution for NCERT class 6-12
Prove that the area of the parallelogram formed by the linesa1x + b1y + c1 = 0, a1x + b1y+ d1 = 0, a2x + b2y + c2 =0, a2x + b2y + d2 = 0 is sq. units.
Deduce the condition for these lines to form a rhombus.
Given:
The given lines are
a1x + b1y+ c1 = 0 … (1)
a1x + b1y+ d1 = 0 … (2)
a2x + b2y+ c2 = 0 … (3)
a2x + b2y+ d2 = 0 … (4)
Let us prove, the areaof the parallelogram formed by the lines a1x + b1y + c1 =0, a1x + b1y + d1 = 0, a2x + b2y+ c2 = 0, a2x + b2y + d2 =0 is sq. units.
The area of theparallelogram formed by the lines a1x + b1y + c1 =0, a1x + b1y + d1 = 0, a2x + b2y+ c2 = 0 and a2x + b2y + d2 =0 is given below:
Hence proved.