A farmer marks four corners of a rectangular vegetable patch on the coordinate plane…

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

Problem

A farmer marks four corners of a rectangular vegetable patch on the coordinate plane by tying coloured flags. The positions of the flags are described below: • Flag

A

4

units to the right of the

y

-axis and

1

unit above the

x

-axis. • Flag

B

8

units to the right of the

y

-axis and

1

unit above the

x

-axis. • Flag

C

8

units to the right of the

y

-axis and

6

units below the

x

-axis. • Flag

D

4

units to the right of the

y

-axis and

6

units below the

x

-axis. Answer the following questions: (a) Write the coordinates of the four flags

A,\,B,\,C

and

D

. (b) Show that opposite sides of

ABCD

are parallel to the coordinate axes. (c) Prove that

ABCD

is a rectangle using only the facts established in part (b) and the equality of corresponding sides inferred from the given descriptions. (d) If another flag

E

is placed exactly at the midpoint of

AD

, write its coordinates explaining each step of your reasoning without using any formula beyond the Class 9 syllabus.

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