# 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 - Mathematics

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

#### Solution

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.

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 6