Let , and be the vertices of a triangle, where is a real…

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

Problem

Let

A(0,0)

B(t,4)

and

C(3,t)

be the vertices of a triangle, where

t

is a real parameter. (i) Derive an expression for

S(t)

, the signed value of twice the area of

\triangle ABC

, in terms of

t

. (ii) Using your expression, determine the set of all real values of

t

for which the triangle is oriented anticlockwise, the set for which it is oriented clockwise, and the value(s) of

t

for which the three points become collinear.