Prove that the lines 3x-4y+5=0, x+2y=3, 3x-4y+15=0 and x+2y=9 form a parallelogram - Maths - Straight Lines

Question

Prove that the lines 3x-4y+5=0, x+2y=3, 3x-4y+15=0 and x+2y=9 form
a parallelogram

Anuradha Sharma · Accepted Answer

Let the equation of lines AB, BC, CD, DA are 3x-4y+5=0, x+2y=3,
3x-4y+15=0, x+2y=9Now, we know that slope of the line ax + by + c =
0, is given by,m = -abSo, slope of AB = 34Slope of CD = 34Slope of
AB = slope of CDSo, AB is parallel to CD and slope of BC=AD=-12So
BC is parallel to ADso, ABCD is a parallelogram