Question

What is the scale factor in the dilation if the coordinates of A' are (-7,6) and the coordinates of C' are (-4,3)

Answer 1

Answer:
1/3

Explanation:
The general rule to get the new dilation coordinate is as follows:
new coordinate = k * old coordinate
where k is the scale factor

For point A:
Xcoordinate of A' = k * Xcoordinate of A
-7 = k * -21
k = -7 / -21
k = 1/3
Ycoordinate of A' = k * Ycoordinate of A
6 = k * 18
k = 6/18
k = 1/3

For point C:
Xcoordinate of C' = k * Xcoordinate of C
 -4 = k * -12
k = -4/-12
k = 1/3
Ycoordinate of C' = k * Ycoordinate of C
3 = k * 9
k = 3/9
k = 1/3

From all of the above, we can conclude that the scale factor is definitely 1/3

Hope this helps :)