Question

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.
the numbers and letters represent the lengths of the sides of the triangles
scale factor =
(type an integer or a simplified fraction.)
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Explanation:

Step1: Calculate scale factor

The scale factor is the ratio of corresponding sides of the image (smaller triangle) to the pre-image (larger triangle). Use the given corresponding sides:
$\text{Scale factor} = \frac{6}{8} = \frac{3}{4}$

Step2: Solve for $x$

Multiply the corresponding side of the larger triangle by the scale factor:
$x = 12 \times \frac{3}{4} = 9$

Step3: Solve for $y$

Multiply the corresponding side of the larger triangle by the scale factor:
$y = 10 \times \frac{3}{4} = \frac{30}{4} = \frac{15}{2}$

Answer:

Scale factor = $\frac{3}{4}$, $x = 9$, $y = \frac{15}{2}$