Let , and be the vertices of a…

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

Problem

Let

G(p,p)

H(5,2)

and

J(3,p+4)

be the vertices of a triangle. (i) Derive the quadratic equation satisfied by

p

if the area of triangle

GHJ

7.5

square units. (ii) Solve the quadratic equation obtained in part (i) and list all real values of

p

. (iii) For each permissible value of

p

, state whether the triangle

GHJ

is isosceles, scalene or right-angled, giving reasons based on side lengths.