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.)
help me solve this view an example get more help .
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Explanation:

Step1: Calculate scale factor

Scale factor = $\frac{\text{side of smaller triangle}}{\text{side of larger triangle}} = \frac{4}{6} = \frac{2}{3}$

Step2: Find length $x$

$x = 9 \times \text{scale factor} = 9 \times \frac{2}{3}$

Step3: Find length $y$

$y = 7 \times \text{scale factor} = 7 \times \frac{2}{3}$

Answer:

Scale factor = $\frac{2}{3}$
$x = 6$
$y = \frac{14}{3}$