Question

What is the scale factor of this dilation? [Not drawn to scale]

Answer 1

How many times bigger is the right triangle than the left triangle?
A side on the right triangle is 15. The same side on the left triangle is 10. 15/10=1.5.
No matter what side you choose on the right triangle and divide it by the corresponding side of the left triangle, you get the same answer: 1.5.
So, the right triangle is 1.5 times larger than the left triangle. This is the scale factor.
What is 1.5 in fraction form?
The answer is left as an exercise for the reader.

Answer 2

Answer:

The scale factor of the dilation is:

                           $1\dfrac{1}{2}$

Step-by-step explanation:

Scale factor--

It is a fixed amount by which the each  of the dimension of the original figure is multiplied in order to obtain the dilated image of the figure.

Here we see that there is a enlargement dilation.

( since the side of the image increases after the dilation)

Let the scale factor be k.

From the figure we see that:

The side of length 6 units is transformed to get a side of length 9 units.

i.e.

$6\times k=9$

i.e.

$k=\dfrac{9}{6}\\\\i.e.\\\\k=\dfrac{3}{2}\\\\i.e.\\\\k=1\dfrac{1}{2}$