Question

Prove that the diagonals of a rectangle bisect each other. Plan: Since midpoints will be involved, use multiples of __ to name the coordinates for B, C, and D.

Answer 1

To prove diagonals of a rectangle bisect each other.

It is always better to take multiple of 2.

For example A(0,0), B( 2 x,0), C(2 x, 4 x), D(0,4 x).where x is any integer.

as,⇒ AB=CD, and BC=AD,[opposite sides are equal]

⇒ Diagonal AC=Diagonal BD

⇒Sides are perpendicular to one another.

So ABCD is a rectangle.

Mid point of AC=
`[(2x+0)/(2),(0+4x)/(2)]`

=(x,2 x)

Mid point of B D=
`[(0+2 x)/(2),(4 x+ 0)/(2)]`

=(x,2x)

Which shows that diagonals of rectangle bisect each other.

If you will take all vertices as a multiple of 6 that will be excellent.