Question

50 POINTS!! ANSWER CORRECTLY PLEASE!

Consider the dilation:
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain.
Answer:

Answer 1

Reduction

Why ?

• See co-ordinates decreased back in dilated figure .

#b

• M=(-3,3)
• M'=(-2,2)
• S=(6,3)
• S'=(4,2)
• V=(3,-3)
• V'=(2,-2)

Scale factor:-

`\\ \rm\rightarrowtail (-2)/(-3)=(4)/(6)=(2)/(3)`

`\\ \rm\rightarrowtail (2)/(3)=(2)/(3)=(2)/(3)`

• Scale factor=K=2/3

Answer 2

The original figure is MSV and the dilated figure is M'S'V'

Therefore, the dilation is a reduction of the original figure since the side lengths have reduced in length.

To determine the scale factor, choose one of the sides and compare the length before and after the dilation → let's use MS:

length of MS = 9 units

length of M'S' = 6 units

⇒ scale factor = length after dilation ÷ length before dilation

= 6 ÷ 9

= 2/3

To find the center of dilation, draw a line through each point and its corresponding dilated point. The point at which the 3 lines meet is the center of dilation.

Therefore, the center of dilation for this question is the origin (0, 0)