NCERT Solutions
Class 11 Maths
Straight Lines

Ex.10.1 Q.9
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
Let points (–2, –1), (4, 0), (3, 3), and (–3, 2) be respectively denoted by A, B, C and D.
Slope of AB = (0 + 1) ÷ (4 + 2) =
Slope of CD = (2 - 3) ÷ (-3 - 3) = (-1) ÷ (-6) =
So, Slope of AB = Slope of CD
=> AB and CD are parallel to each other.
Now, slope of BC = (3 - 0) ÷ (3 - 4) = 3 ÷ (-1) = -3
Slope of AD = (2 + 1) ÷ (-3 + 2) = 3 ÷ (-1) = -3
=> Slope of BC = Slope of AD
=> BC and AD are parallel to each other.
Therefore, both pairs of opposite sides of quadrilateral ABCD are parallel. Hence, ABCD is a parallelogram.
Thus, the points (–2, –1), (4, 0), (3, 3), and (–3, 2) are the vertices of a parallelogram.