Answer:
length of image of AB is 4 inches.
Step-by-step explanation:
Scale factor(k) is defined as the ratio of image to the pre-image.
i.e,
\(k = \frac{\text{Image}}{\text{Pre-image}}\)
as per the statement:
The length of AB is 10 inches. A dilation with a scale factor of \(\frac{2}{5}\)
⇒ \(k= \frac{2}{5} =0.4\) and Length of pre-image AB = 10 inches.
by definition of scale factor:
\(\text{length of image AB} = k \cdot \text{Length of Pre-image AB}\)
Substitute the given values we have;
\(\text{length of image AB} = 0.4 \cdot 10\)
Simplify:
\(\text{length of image AB} =4\) inches.
Therefore, the length of image AB is 4 inches.
