The vertices of are

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

Problem

The vertices of

\triangle ABC

are

A(1,2)

B(7,4)

and

C(5,10)

. A point

D

divides

BC

externally in the ratio

3:2

(that is,

BD:DC=3:2

). (i) Find the coordinates of

D

. (ii) Calculate the area of

\triangle ABC

. (iii) Calculate the area of

\triangle ABD

. (iv) Hence determine the ratio

\displaystyle \dfrac{\text{area}(\triangle ABD)}{\text{area}(\triangle ABC)}

and state which triangle has the larger area.