Question

Find the images vertices for a dilation with center(0,0) and a scale factor of 4.

Answer 1

@malcolmmcswain i dont know how to find vertices can you help

Answer 2

This is a tricky one.

Answer 3

I know an easy, but complicated way to do this.

Answer 4

Wanna try it?

Answer 5

ok lets see if i can follow that way

Answer 6

Never mind. I have a waaayyyyy easier way. But before I show you it, I need to explain how it works:

Let's start off with this figure here:

https://www.desmos.com/calculator/lttgxf6exs

Answer 7

Oops sorry wrong link

Answer 8

https://www.desmos.com/calculator/ue9blhj06i

Answer 9

There's your figure.

Answer 10

Now, let's take the point (4,-3)

Answer 11

ok

Answer 12

And expand it outwards along a line, like this:
https://www.desmos.com/calculator/kvjqstpl7y
If the take the distance between the point and the origin (0,0) like this:

Answer 13

Are you following?

Answer 14

i cant read the drawing

Answer 15

It says if the distance between the point and the origin is n, then the translated points distance from the origin will be 4 * n

Answer 16

(if we are using a scale factor of 4)

Answer 17

ok i got that

Answer 18

To find n we need x and y.

Answer 19

what is x and y

Answer 20

So, if we let theta be the scale factor.
The translated point will be:

\[((x \times \theta),(y \times \theta)\]

Answer 21

So, for a scale factor of 4, we can find each translated vertex with (x*4),(y*4)

Answer 22

im confused where do you get x and y

Answer 23

x and y are what you use to get coordinates...

Answer 24

ok but what are referring to as x and y

Answer 25

Ok. Let me help you visualize. Instead of theta, let's use s to represent the scale factor.

Answer 26

ok

Answer 27

https://www.desmos.com/calculator/vjvbnc5dnv

The green points represent the preimage.
The blue points represent the dilated image.
S represents the scale factor. When we change s, we change the dilation. Play around with it a bit until you understand.