Question

△qrs is the image of △qrs under a dilation through point c. what scale factor was used in the dilation? -4 -0.25 0.25 4

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\).

Step2: Identify the lengths

Let's assume we use the segments \(SS'\) (or any corresponding segments). The length of the pre - image segment (e.g., if we consider the side related to the smaller triangle) is \(3\mathrm{cm}\), and the length of the image segment (related to the larger triangle) is \(12\mathrm{cm}\). Also, note the direction: the image is on the opposite side of the center of dilation \(C\) compared to the pre - image, so the scale factor is negative.

$$k =-\frac{12}{3}$$

Step3: Calculate the scale factor

$$k=- 4$$

Answer:

\(-4\) (i.e., the first option \( - 4\))