Answer: (2, 4)
Step-by-step explanation
Let C be the center of dilation.
C = (1,2)
The horizontal distance from C to A is 2 units. The scale factor 1/2 will make this horizontal distance to be (1/2)*2 = 1 unit.
The vertical distance from C to A is 4 units. Cut this in half to get (1/2)*4 = 2 which is the new vertical distance.
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Recap so far:
To go from C to A we follow the pathway "right 2, up 4"
To go from C to A', we need to follow the pathway "right 1, up 2", where each value is half of the previous values.
Start at C(1,2). Move right 1 and up 2 and you should arrive at A ' (2, 4)
See the diagram below.