Question

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

What is the scale factor used to create the dilation?

Answer 1

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

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=\frac{\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=√((-4+4)^2+(-6+4)^2)=√(0+4)=2`

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

`d_2=√((-4+4)^2+(2+4)^2)=√(0+36)=6`

Therefore, the scale factor of dilation is

`S=(d_2)/(d_1)=(6)/(2)=3.`

Thus, the required scale factor of dilation is 3.