Question

Rectangle M was dilated to form rectangle M’.

What ratio is the scale factor?
A. 1/2
B. 2/3
C. 4/3
D. 3/2

Answer 1

Answer: The correct option is (D)
`(3)/(2).`

Step-by-step explanation: Given that rectangle M was dilated to form rectangle M'.

We are to select the ratio that is the scale factor of dilation.

We know that

the scale factor of dilation is defined as follows :

`S=\frac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.`

In the given dilation, we have

length of a side of the original rectangle = 4 units

and

the length of the corresponding side of the dilated rectangle = 6 units.

Therefore, the required scale factor of dilation is given by

`S=(6)/(4)\\\\\\\Rightarrow S=(3)/(2).`

Thus, option (D) is CORRECT.

Answer 2

Hey!

The length of the small rectangle is 4. The length of the big rectangle is 6.

Since the smaller rectangle was dilated to make a bigger rectangle, the scale factor will be more than 1. To find the scale factor, you have to divide the length of a side of the original rectangle by the length of a side of the new rectangle.

`Scale \hspace{1 mm} Factor = (Length\ Of\ Original \ Rectangle)/(Length\ Of\ New\ Rectangle) = (6)/(4)`

Simplify:

`(6 / 2)/(4 / 2) = (3)/(2)`

The scale factor is
`(3)/(2)` and the choice that matches it is choice D.

`\framebox{Answer = D}`