Question

Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram.

Answer 1

The given points are A(–4, –7), B(–1, 2), C(8, 5) and D(5, –4). 
Slope of AB = \[\frac{2 - \left( - 7 \right)}{- 1 - \left( - 4 \right)} = \frac{9}{3} = 3\]

Slope of BC = \[\frac{5 - 2}{8 - \left( - 1 \right)} = \frac{3}{9} = \frac{1}{3}\]

Slope of CD = \[\frac{- 4 - 5}{5 - 8} = \frac{- 9}{- 3} = 3\]

Slope of AD = \[\frac{- 4 - \left( - 7 \right)}{5 - \left( - 4 \right)} = \frac{3}{9} = \frac{1}{3}\]

Slope of AB = Slope of CD
Slope of BC = Slope of AD
So, AB || CD and BC || AD
Hence, ABCD is a parallelogram.