The points and are fixed in the plane

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

Problem

The points

A(7,-3)

and

B(-1,5)

are fixed in the plane. A variable point

P(x,y)

divides

AB

in the ratio

\lambda:1

(with

\lambda\neq -1

) and satisfies the condition

x + y = 4

. (i) Express

x

and

y

in terms of

\lambda

. (ii) Using the given condition, determine the possible value(s) of

\lambda

. (iii) Hence find the corresponding coordinates of

P

. (iv) For each value of

\lambda

obtained, state whether the division is internal or external and justify your answer.