Question

Rectangle M was dilated to form rectangle M’.

Rectangle M has a length of 4 and width of four-thirds. Rectangle M prime has a length of 6 and width of 2.

What ratio is the scale factor?
One-half
Two-thirds
Four-thirds
Three-halves

Answer 1

To find the scale factor of the dilation from rectangle M to rectangle M', we can compare the corresponding sides of the two rectangles.

First, let's identify the dimensions of both rectangles:

- Rectangle M: Length = 4, Width = \(\frac{4}{3}\)
- Rectangle M': Length = 6, Width = 2

Now we will calculate the scale factor (k) for both the length and width.

1. **Calculating the scale factor for length:**
\[
k = \frac{\text{Length of M'}}{\text{Length of M}} = \frac{6}{4} = \frac{3}{2}
\]

2. **Calculating the scale factor for width:**
\[
k = \frac{\text{Width of M'}}{\text{Width of M}} = \frac{2}{\frac{4}{3}} = 2 \times \frac{3}{4} = \frac{3}{2}
\]

In both cases, the scale factor is \(\frac{3}{2}\).

Thus, the ratio that represents the scale factor is \( \frac{3}{2} \), which corresponds to "Three-halves."