On a field represented by a Cartesian grid

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

Problem

On a field represented by a Cartesian grid, three wells are marked as follows: • Well

A

is at the intersection of the lines

x=-4

and

y=2

. • Well

B

is at the intersection of the vertical line that is

6

units to the right of Well

A

and the horizontal line that is

5

units below Well

A

. • Well

C

lies on the same horizontal line as Well

B

but on the

y

-axis. (i) Write the coordinates of wells

A

B

and

C

. (ii) Plot the three wells on a Cartesian plane and join them to form

\triangle ABC

. (iii) Using the axes as reference, determine the base and height of

\triangle ABC

and hence find its area. (iv) State whether

\triangle ABC

is right-angled, giving a reason based only on the orientation of its sides with respect to the axes.