Answer:
The rule of dilation centered at the origin is (x , y) → (2x , 2y) ⇒ answer A
Step-by-step 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)
