A rectangular garden is laid out on a coordinate grid such that its south-west corner…

MATHEMATICS · Subjective · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

A rectangular garden is laid out on a coordinate grid such that its south-west corner is at the origin

O(0,0)

. Each unit on the grid represents

1

metre. The positions of certain objects in the garden are described below: • A mango tree

M

9

metres east of

O

and

2

metres north of the

x

-axis. • A rose bush

R

4

metres west of the

y

-axis and

2

metres north of the

x

-axis. • A fountain

F

9

metres east of

O

and

6

metres south of the

x

-axis. Answer the following: (i) Write the coordinates of

M

R

and

F

. (ii) Show that the line segment joining

M

and

F

is parallel to the

y

-axis, and the line segment joining

M

and

R

is parallel to the

x

-axis, giving suitable reasons based on their coordinates. (iii) If a bench

B

has to be placed exactly midway between

M

and

R

along the line segment

MR

, determine the coordinates of

B

without using any formula beyond what you have learnt in Class 9.