Question

part 1 of 3
in the following figure, the smaller triangle is the image of the larger triangle under a dilation centered at point o. find the scale factor and the length of x and y as pictured.
scale factor =
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate scale factor

The scale factor is the ratio of corresponding side lengths of the image (smaller triangle) to the pre-image (larger triangle). Use the given corresponding sides:
$\text{Scale factor} = \frac{6}{12} = \frac{1}{2}$

Step2: Find length of x

Use the scale factor on the corresponding side of length 8:
$x = 8 \times \frac{1}{2} = 4$

Step3: Find length of y

Use the scale factor on the corresponding side of length 10:
$y = 10 \times \frac{1}{2} = 5$

Answer:

Scale factor = $\frac{1}{2}$
$x = 4$
$y = 5$