Question

A dilation has center(0,0,0). Find the image of the point (-1,-2,0) for the scale factor of 3.

Answer 1

@malcolmmcswain

Answer 2

Hold on. I'll be right back.

Answer 3

ok

Answer 4

Is this a 3-dimensional plane, or did you make a typo? Just asking, because I don't often see three-dimensional planes used in Euclidean, and so far that's all you've posted... -_-

Answer 5

If it is a 3D plane, then a dilation by a factor of 3 would be:

\[(x \times 3, y \times 3, z \times 3)\]

I believe...

Answer 6

@lochana I see you're watching. Do you agree?

Answer 7

yes. I think so

Answer 8

but wait

Answer 9

A dilation by a factor of n is just all the coordinates multiplied by n, right?

Answer 10

wouldn't it be like that?

Answer 11

So you're saying we don't have to multiply z?

Answer 12

yes. and don't just multiply x and y by 3 either.

Answer 13

you need scale up first and then find x and y coordinates. let me show you

Answer 14

help me
Point A is located at negative 7 over 10 and point B is located at negative 2 over 10. What is the distance between points A and B?

Answer 15

Ok... I think I see what you mean.

Answer 16

\[OA = \sqrt{(-2)^2 + (-1)^2} = \sqrt{5}\]

Answer 17

now multiply OA by 3. which is \[3\sqrt{5}\]

Answer 18

Ok, I get it now!

Answer 19

3D graphs are confusing...

Answer 20

The total temperature change over 3 days in Gritty City was −6 degrees Celsius.

What was the average temperature change each day?

Answer 21

and yes. if we think about proportionality, you end up getting 3x and 3y:)

Answer 22

@malcolmmcswain you are correct x and y must be multiplied by 3

Answer 23

Yeah, I'm kind of thinking about it more on a cartesian plane.

Answer 24

answer is (-3, -6, 0)