Question

Which rule yields the dilation of the figure KLMN centered at the origin?

A) (x, y) → (2x, 2y)
B) (x, y) → (1/2x, 1/2y)
C) (x, y) → (x + 2, y + 2)
D) (x, y) → (x + 1/2, y + 1/2)

Answer 1

Answer: A) (x, y) → (2x, 2y)

The pre-image is enlarged. The coordinates of KLMN have been multiplied by 2.

Answer 2

The rule of dilation centered at the origin is (x , y) → (2x , 2y) ⇒ answer A

Explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.

- It can become larger or smaller, but the shape of the

figure does not change.

- The scale factor, measures how much larger or smaller

the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- The dilation rule for any point (x , y) is (kx , ky), where k is the

factor of dilation centered at origin

* Now lets solve the problem

- The figure KLMN has for vertices:

K (3 , -3) , L (3 , 4) , M (5 , 4) , N (5 , -3) ⇒ (1)

- The image K'L'M'N' of figure KLMN after dilation about the origin

has four vertices:

K' (6 , -6) , L' (6 , 8) , M' (10 , 8) , N' (10 , -6) ⇒ (2)

- From (1) and (2)

# (3 , -3) ⇒ (6 , -6)

# (3 , 4) ⇒ (6 , 8)

# (5 , 4) ⇒ (10 , 8)

# (5 , -3) ⇒ (10 , -6)

- Each point in KLMN multiplied by 2

∴ The scale of dilation is 2

∴ The rule of dilation centered at the origin is (x , y) → (2x , 2y)