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

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

Answer:-

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.

Chapter 5. Co-ordinate Geometry – Practice Set 5.3 (Page 121)