The vertices of a triangular plot of land are

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

Problem

A(-3,-1)

B(5,2)

and

C(1,7)

. Two pegs are driven into the ground at points

Q(2,3)

and

R(3,5)

. (i) Compute the area of

\triangle ABC

. (ii) For the point

Q

, find the areas of

\triangle QAB

\triangle QBC

and

\triangle QCA

, and hence decide whether

Q

lies inside, on an edge of, or outside the triangular plot. (iii) Repeat part (ii) for the point

R

. (iv) Compare the locations of

Q

and

R

with respect to

\triangle ABC

, clearly stating your conclusions.