Question

On the coordinate plane, the origin is the center of an expansion with a scale factor of m. How would you express the coordinates of the image points for pre-image points (3, -7) in terms of m?

A segment with endpoints (2, 5) and (4, -1) is dilated to the image segment with endpoints (10, 25) and (20, -5). What is the scale factor for the dilation?

Answer 1

dilation with origin as center :

\(\large (x, y) \to (mx, my)\)

Answer 2

whaaa... I don't get it English please heheeheh

Answer 3

\(\large (3, -7) \to (3m, -7m)\)

Answer 4

to dilate by a scale factor of \(m\) , just multiply both x and y coordinates by \(m\)

Answer 5

So what is my next step here? or is that all?

Answer 6

thats all for the first part

Answer 7

Oh, what about the other part :)
I'm probably annoying you by now sorry, Almost done with my assignment

Answer 8

and by almost done I mean 7 left :(

Answer 9

just take the ratio of any image coordinate to the pre-image coordinate :
scale factor = \(\dfrac{10}{2} = 5\)

Answer 10

wait im lost, could you break it down for me?

Answer 11

take any point, say : (2, 5)
and the corresponding image : (10, 25)

Answer 12

from first part, wat do u knw about the rule for dilation ?

Answer 13

you multiply both sides

Answer 14

Yes, dilation rule is :

\(\large (x, y) \to (mx, my)\)

right ?

Answer 15

Yes

Answer 16

\(\large (2, 5) \to (10, 25)\)

Answer 17

\(\large (2, 5) \to (2m, 5m)\)

Answer 18

\(\large \implies 2m = 10 \)

Answer 19

\(\large m = \dfrac{10}{2} = 5\)

Answer 20

you just need to figure out the number that u need to multiply to get to 10 from 2

Answer 21

So Is that what I write? Or just just your example

Answer 22

below work is sufficient :

(2, 5) --> (10, 25)
so scale factor = 10/2 = 25/5 = 5

Answer 23

Thank you a million times @ganeshie8
Have a nice night!!

Answer 24

you too :)