Question

Prove that the diagonals of a rectangle ABCD with vertices A(2, –1), B(5, –1), C(5, 6) and D(2, 6) are equal and bisect each other.

Answer 1

The vertices of the rectangle ABCD are A(2, -1), B(5, -1), C(5, 6) and D(2, 6) Now,

`"Coordinates of midpoint of" AC = ((2+5)/2 , (-1+6)/2) = (7/5 ,5/2)`

`"Coordinates of midpoint of " BD = ((5+2)/2 , (-1+6)/2)= (7/2,5/2)`

Since, the midpoints of AC and BD coincide, therefore the diagonals of rectangle ABCD bisect each other.