Question

Q29. PQRS is a rectangle, point 1
of intersection of diagonals is
origin and PQ = 2a units and QR
= 2b units. The coordinates of
all of its vertices are​

Answer 1

Given :

PQRS is a rectangle.

Length of PQ = 2a units

Length of QR = 2b units

Point of intersection of the diagonals PR and SQ is the origin (0, 0).

To find :

Coordinates of the vertices of the rectangle ABCD.

Solution:

Since diagonals of a rectangle bisect each other.

Point of intersection of both the diagonals will be the midpoint of the diagonals.

Axes x-axis and y-axis will bisect the sides PQ and RS.

As shown in the attachment,

Coordinates of extreme ends of the diagonal QS will be,

Q(a, b) and S(-a, -b)

Similarly, coordinates of the extreme ends of the other diagonal PR will be,

P(-a, b) and R(b, -a)

We can check that midpoint of the diagonals of rectangle PQRS is,

$[\frac{(a-a)}{2},\frac{b-b}{2}]$ → (0, 0)

Therefore, four vertices of the rectangle will be P(-a, b), Q(a, b), R(b, -a) and S(-a, -b).