Question

the triangle abc is a dilation of the triangle abc. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find coordinates of corresponding points

Let's take point \(B(0,3)\) and \(B'(0,4)\). But better to use horizontal or vertical segments. Take \(BC\): \(B(0,3)\), \(C(3,3)\) so \(BC = 3-0= 3\) units. \(B'C'\): \(B'(0,4)\), \(C'(4,4)\) so \(B'C'=4 - 0=4\) units.

Step2: Calculate scale factor

Scale factor \(k=\frac{\text{length of dilated segment}}{\text{length of original segment}}\). Using \(BC\) and \(B'C'\), \(k = \frac{4}{3}\)

Answer:

\(\frac{4}{3}\)