Question

A(2, 5), B(1, 0), C(−4, 3) and D(–3, 8) are the vertices of quadrilateral ABCD. Find the co-ordinates of the mid-points of AC and BD. Give a special name to the quadrilateral.

Answer 1

Co-ordinates of A = (2, 5), of B = (1, 0), of C = (−4, 3) and of D = (−3, 8)

Let the mid-point of AC is P(x₁, y₁)

∴ Co-ordinates of mid-point of AC will be

`(x_1, y_1) = ((2 - 4)/2, (5 + 3)/2)`

=`((-2)/2, 8/2)`

= (−1, 4)

Let the mid-point of BD is Q(x₂, y₂)

Co-ordinates of mid-point of BD will be

∴ `(x_2, y_2) = ((1 + (-3))/2, (0 + 8)/2)`

= `((1 - 3)/2, 8/2)`

= `((-2)/2, 8/2)`

= (−1, 4)

∵ Co-ordinates of mid-points AC and BD are the same.

∴ The quadrilateral is a parallelogram.