The point is the intersection of the lines 3x-y=7 and x+y=5

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

Problem

The point

P

is the intersection of the lines

3x-y=7 \quad \text{and} \quad x+y=5.

Let

Q(6,2)

and

R(6,-4)

be two other points in the plane. (i) Determine the coordinates of

P

. (ii) Using

P

Q

and

R

as vertices, calculate the area of triangle

PQR

. (iii) Find the length of side

QR

and hence obtain the perimeter of triangle

PQR

. (Leave

\sqrt{5}

in your answer if it occurs.)