Answer:
(a) 1/5
Step-by-step explanation:
The scale factor multiplies each coordinate of the preimage to give the corresponding image coordinate.
Application
Let the scale factor be represented by k. Then we have ...
G'(2, 2) = k×G(10, 10)
For the x-coordinates, this is ...
2 = k×10
2/10 = k = 1/5 . . . . . . divide by the coefficient of k
Similarly, for the y-coordinates, ...
2 = k×10
2/10 = k = 1/5
(We expect the x- and y-scale factors to be the same.)
The scale factor is 1/5.
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Additional comment
If the scale factor were -1/5, point G' would be ...
G' = (-1/5)G = (-1/5)(10, 10) = (-2, -2)
This is the location of J', on the other side of the origin from G.
A negative scale factor not only changes the scale, but also reflects across the center of dilation.
