Points and are fixed vertices of a triangular park

MATHEMATICS · Multi-part · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

Points

A(2,1)

and

C(10,5)

are fixed vertices of a triangular park. The third vertex

B

must lie on the straight line

3x + 4y = 20

such that

\angle B

is a right angle. (i) Find all possible coordinates of

B

that satisfy the given condition. (ii) For each position of

B

obtained in part (i), calculate the area of

\triangle ABC

. Comment on whether the two areas are equal, giving reasons for your answer.