Question

1. what is the result of applying a dilation with a scale factor of 3 to a rectangle with side lengths of 2 units and 4 units?

a. the new rectangle has side lengths of 9 units and 18 units.
b. the new rectangle has side lengths of 6 units and 12 units.
c. the new rectangle has side lengths of 4 units and 8 units.
d. the new rectangle has side lengths of 3 units and 6 units.

Explanation:

Step1: Recall dilation formula

When dilating a figure with a scale factor \(k\), new length = original length \(\times k\).

Step2: Calculate new side - length 1

For the side with original length \(a = 2\) units and \(k = 3\), new length \(a_{new}=2\times3 = 6\) units.

Step3: Calculate new side - length 2

For the side with original length \(b = 4\) units and \(k = 3\), new length \(b_{new}=4\times3 = 12\) units.

Answer:

B. The new rectangle has side lengths of 6 units and 12 units.