Question

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

Answer 1

We know that, slope of line = `(y_2 - y_1)/(x_2 - x_1)`

Slope of side AB = `(2 - (-7))/(-1 - (-4))`

= `(2 + 7)/(-1 + 4)`

= `9/3`

= 3    ......(i)

Slope of side BC = `(5 - 2)/(8 - (-1))`

= `3/(8 + 1)`

= `3/9`

= `1/3`  ......(ii)

Slope of side CD = `(-4 - 5)/(5 - 8)`

= `(-9)/(-3)`

= 3       .....(iii)

Slope of side AD = `(-4 - (-7))/(5 - (-4))`

= `(-4 + 7)/(5 + 4)`

=`3/9`

= `1/3`   ......(iv)

∴ Slope of side AB = Slope of side CD   ......[From (i) and (iii)]

∴ Side AB || side CD

∴ Slope of side BC = Slope of side AD   .......[From (ii) and (iv)]

∴ Side BC || side AD

Both the pairs of opposite sides of ABCD are parallel

∴ ▢ABCD is a parallelogram.

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