A farmer owns a rectangular field whose four vertices

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

Problem

A farmer owns a rectangular field whose four vertices, in order, are

A(1,1)

B(1,9)

C(13,9)

and

D(13,1)

. He plans to lay an underground water pipeline along the diagonal

AC

and install a pump at a point that divides the diagonal in the ratio

3:2

measured from

A

C

. (i) Calculate the exact length of the diagonal

AC

. (ii) Determine the coordinates of the point

T

where the pump will be placed. (iii) The farmer also wants to run a control cable from the pump at

T

to the midpoint

M

of the side

CD

. Find the length of this cable.