Pre-image point n(6, -3) was dilated to point n'(2, -1). what was the scale factor used?
what is the midpoint between (-8, 5) and (2, -2)?

Question 1

Let the scale factor be k.

Then, we have the mapping

This implies that:

We equate any corresponding component find the value of the scale factor k.

6k=2

Hence the scale factor is  

Question 2:

The midpoint of any two points can be calculated using the formula;

We want to find the midpoint of (-8, 5) and (2, -2).

The midpoint is:

Scale Factor = (-4,2)

Mid-point = (-3, 3/2)

Step-by-step explanation:

Let X = (x,y) be the scale factor by which the point was dilated. Using this assumption we can write that:

N+X=N^'

(6,-3)+(x,y)=(2,-1)

(6+x,-3+y)=(2,-1)

Putting the coordinates equal one by one:

For x-coordinate:

6+x=2

x=2-6

x= -4

For y-coordinate:

-3+y= -1

y= -1+3

y=2

So the scale factor was:

(-4,2)

For the mid-point of (-8,5) and (2,-2)

Mid-point=((-8+2)/2,(5-2)/2)

=((-6)/2,3/2)

=(-3,3/2)

answer:

at time x=0 we have 1000, at time x=1 we have 2000, at time x=2 we have 4000.  

so that's an initial value of 1000 and a ratio of 2,

y = 1000 (2^x)

hope this !