Exercise 121 Page 264

Practice makes perfect

a Let's begin by plotting the coordinates of △ ABC.

To enlarge the polygon so that the ratio of the side lengths is 3, we have to triple the distance of each vertex from the origin and in the same direction. We can do this by multiplying each point's coordinates by 3.

(x,y)	( 3x, 3y)	=
(- 1,- 1)	( 3(- 1), 3(- 1))	(- 3,- 3)
(3,- 1)	( 3(3), 3(- 1))	(9,- 3)
(- 1,- 2)	( 3(- 1), 3(- 2))	(- 3,- 6)

When we know the coordinates of A', B' and C', we can draw △ A'B'C'.

b A rotation of a polygon 90^(∘) clockwise about the origin is the same thing as rotating the polygon by 270^(∘) counterclockwise. The coordinates of the figures vertices will change in the following way.

preimage (a,b)→ image (b,- a)

Using this rule on the vertices of A'B'C', we can find the vertices of A''B''C''.

Point	(a,b)	(b,- a)
A'	(- 3,- 3)	(- 3,3)
B'	(9,- 3)	(- 3,- 9)
C'	(- 3,- 6)	(- 6,3)

When we know the coordinates of A'', B'' and C'', we can draw △ A''B''C''.

c To determine the translation that moves A to (5,3), we need to find the vertical and horizontal difference between A and (5,3).

From the diagram, we see that A has been translated 4 units in the positive vertical direction and 6 units in the positive horizontal direction. Since a translation is a rigid motion, we have to perform the same vertical and horizontal translation on B.