Question

1. is the scale factor of the dilation of △abc equal to ½? explain.
2. square a is a dilation of square b.

what is the scale factor?
a. 1/7
b. 5/4
c. 4/5
d. 7
e. 25/16

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is the ratio of the side length of the image (square \(A\)) to the side length of the pre - image (square \(B\)). If the side length of square \(A\) is \(s_A\) and the side length of square \(B\) is \(s_B\), then \(k=\frac{s_A}{s_B}\).

Step2: Identify the side lengths

From the problem, \(s_A = 35\) and \(s_B=28\).

Step3: Calculate the scale factor

Substitute the values into the formula: \(k=\frac{35}{28}\). Simplify the fraction \(\frac{35}{28}=\frac{5\times7}{4\times7}=\frac{5}{4}\) (divide both the numerator and the denominator by their greatest common divisor, which is \(7\)).

Answer:

\(\frac{5}{4}\) (option c)