Let and be two fixed points

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

Problem

Let

A(2,-1)

and

B(-1,3)

be two fixed points. A variable point

C(k,4)

lies on the horizontal line

y=4

, and another variable point

D(5,k)

lies on the vertical line

x=5

, where

k

is a real parameter. Triangles

\triangle ABC

and

\triangle ABD

are formed. (i) Obtain expressions for the areas of

\triangle ABC

and

\triangle ABD

in terms of

k

. (ii) Find all value(s) of

k

for which the two triangles have equal area. (iii) Determine the ratio

\displaystyle \text{area}(\triangle ABC):\text{area}(\triangle ABD)

when

k=7