Question

Suppose that rectangle ABCD is dilated to A'B'C'D' by a scale factor of 2.5 with a center of dilation at the origin.

What is the distance from the center of dilation to the midpoint of A'B'?
A) 2.5 units
B) 7.5 units
C) 10 units
D) 17.5 units

Answer 1

Rectangle ABCD is dilated to A'B'C'D' by a scale factor of 2.5 with a center of dilation at the origin.

So, when a figure is dilated and dilation>1, the size of shape increases. and the two shapes are identical i.e similar.

So,$\frac{A'B'}{AB}=\frac{C'B'}{CB}=\frac{C'D'}{CD}=\frac{A'D'}{AD}=2.5$

Let O be the center of Dilation.

If O A=5, then O A'=2.5 ×5=12.5, Let AB=8, then A'B'=2.5× 8=20

Let mid point of AB is M and mid point of A'B' is N.

So, AM=4 And A'N=10

 In Δ O A M, OM⊥AB  ,Applying pythagoras theorem

5²=4²+AM²→AM=3

∴ AN=3×2.5=7.5 units

Or

In Δ O A' N  ON⊥A'B'  ,Applying pythagoras theorem

12.5²=10²+ON²→ON²=156.25-100→ON²=56.25→ON²=7.5²→ON=7.5

Distance from the center of dilation to the midpoint of A'B=7.5 units.

Option (B) is correct.

Answer 2

Answer:

thank you

Step-by-step explanation: