Let be any triangle whose vertices are

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

Problem

Let

\triangle ABC

be any triangle whose vertices are

A(x_1,y_1)

B(x_2,y_2)

and

C(x_3,y_3)

. (i) Show that if every

x

-coordinate is multiplied by a constant

a

and every

y

-coordinate by a constant

b

(where

a,b\neq 0

), then the area of the resulting triangle is

|ab|

times the area of

\triangle ABC

. (ii) Prove that adding a constant vector

(h,k)

to every vertex does not change the area of the triangle. (iii) A triangle with vertices

(1,2)

(4,1)

and

(3,5)

is first stretched so that

x

-coordinates are doubled while

y

-coordinates are tripled, and is then translated by

(7,-4)

. Compute the final area and verify your results using the conclusions of parts (i) and (ii).