Question

The dashed triangle is the image of the solid triangle. The center of dilation is (-4, -4)

Answer 1

Answer:

See below and you can do it for yourself. You can catch me a fish too.

Step-by-step explanation:

Work out what multiplication is needed to make the sides the same length. I'd go for the short edge.

The decide if it is a positive or negative scaling. Negative gives a mirror whereas positive looks the same as the original.

Answer 2

Answer:  The required scale factor of dilation is 3.

Step-by-step explanation:  Given that the dashed triangle is the image of the solid triangle and the center of dilation is (-4, -4).

We are to find the scale factor that is used to create the dilation.

We know that the scale factor of dilation is given by

$S=\dfrac{\textup{length of a side of the dilated triangle}}{\textup{length of the corresponding side of the original triangle}}.$

From the graph, we note that

two vertices of the original triangle are (-4, -4) and (-4, -6).

And, the corresponding two vertices of the dilated triangle are (-4, -4)and (-4, 2).

So, the length of a side of the original triangle, as calculated using distance formula is

$d_1=\sqrt{(-4+4)^2+(-6+4)^2}=\sqrt{0+4}=2$

and the length of the corresponding side of the dilated triangle is

$d_2=\sqrt{(-4+4)^2+(2+4)^2}=\sqrt{0+36}=6$

Therefore, the scale factor of dilation is

$S=\dfrac{d_2}{d_1}=\dfrac{6}{2}=3.$

Thus, the required scale factor of dilation is 3.