What is the scale factor (k) of the dilation if C is (-6,9) and C' is (-2,3)?

Step-by-step explanation:

Given the original coordinate as C (-6, 9) and new coordinates after dilation as C' (-2, 3), we can see that the value of the new coordinates has reduces by a factor. Let the factor be k

For the x coordinates:

C' = kC

x' = kx

-2 = k(-6)

-2 = -6k

Divide both sides by -6

k = -2/-6

k = 1/3

For the y-coordinates:

y' = ky

3 = 9k

Divide both sides by 9:

3/9 = 9k/9

1/3 = k

k = 1/3

Hence the scale factor of the dilation is 1/3

The scale factor from C' to C is

3

But the scale factor from C to C' (the one you may have asked for in the question) is

Step-by-step explanation:

What we already know is that we have line segments C and C' and we know their lengths.

C = (-6, 9)

C' = (-2, 3)

So the scale factor from C' to C can be easily known if we simply use the rules of division

-6 ÷ -2

and

9 ÷ 3

They both are equal to the outcome, 3.

So we now know that the scale factor from C' to C is 3.

But what about C to C'??

Yes we still have to do division, BUT (you may have guessed it already but), we must switch the positions that the numbers for dividend and divisor were.

-2 ÷ -6 =

0.33333333...  or  

3 ÷ 9 =

0.33333333...  or  

So we can decisively conclude that the scale factor of C to C' is

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f-1(x)= cube root of 19x squared/x

step-by-step explanation:

the correct answer is the second option