Question

The coordinates of quadrilateral ABCD are A(-1,5),B(8,2),C(11,13),D(2,6).
The midpoint of AC is .....,.......
The midpoint of BD is ......,.......
The slope of AC is .........,
The slope of BD is .........,
Is quadrilateral ABCD is a rhombus ?[Y,N]----.

Answer 1

mid point of AC = (-1+11/2, 5+13/2) = (10/2, 18/2) = (5,9)

Mid point of BD = (8+2/2, 2+6/2) = (10/2, 8/2) = (5,4)

Slope of AC = 13-5/11+1 = 8/12 = 2/3.

slope of BD = 6-2/2-8 = 4/-6 = -2/3

We know that rhombus has a common mid point of its diagonals and product of slopes = -1., not observed here.

conclusion = ABCD not a rhombus

Answer 2

many many thanks