Let , and be the vertices of a triangle and let be a point in the…

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

Problem

Let

A(1,2)

B(7,4)

and

C(4,-2)

be the vertices of a triangle and let

P(4,1)

be a point in the plane. (i) Find the numerical value of the area of

\triangle ABC

. (ii) Calculate the areas of

\triangle PAB

\triangle PBC

and

\triangle PCA

. (iii) Using your results, determine whether

P

lies inside

\triangle ABC

, on its boundary, or outside it. Give suitable numerical justification.