Let have vertices

MATHEMATICS · Subjective · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Let

\triangle XYZ

have vertices

X(1,2)

Y(4,2)

and

Z(1,5)

. Two successive transformations are applied: 1. Rotation

R

(x,y) \mapsto (-y,\,x)

. 2. Scaling

S

(x,y) \mapsto (4x,\,y)

. (i) Find the coordinates

X',Y',Z'

obtained after applying

R

X,Y,Z

. (ii) Calculate the area of

\triangle X'Y'Z'

. (iii) Apply

S

to the points found in part (i) and obtain the coordinates

X'',Y'',Z''

. (iv) Determine the area of

\triangle X''Y''Z''

and express it as a multiple of the area of the original triangle

\triangle XYZ