A rectangular garden is to be drawn on a coordinate grid

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

A rectangular garden is to be drawn on a coordinate grid. Two opposite vertices of the rectangle are

A(2,1)

and

C(8,6)

. The sides of the rectangle are parallel to the coordinate axes. (i) Plot the points

A

and

C

on graph paper. (ii) Determine the coordinates of the remaining two vertices

B

and

D

so that the vertices appear in the order

A,\,B,\,C,\,D

while moving clockwise. (iii) Plot the points

B

and

D

and complete the figure of the rectangle, labelling all vertices. (iv) Verify that

ABCD

is a rectangle by comparing the lengths of its sides, using only the differences in the respective coordinates.