Answer: Choice A
The point Z ' is at (8,4)
The point Y ' is at (0,4)
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Step-by-step explanation:
The key thing here is that point Z does not move. Why not? Because this is where the center of dilation occurs. The center point is fixed. Everything around the center will expand away from, or contract toward, the center.
In this case, the scale factor is 4/5 = 0.8 which is less than 1. So points will contract toward the center. The old pre-image shrinks to make the image smaller.
Note how point Y = (-2,4) is 10 units away from point Z. You can count out the spaces or subtract the x coordinates. Use an absolute value to make sure the result is positive
|x1-x2| = |-2-8| = |-10| = 10
|x2-x1| = |8-(-2)| = |8+2| = |10| = 10
So 0.8 times this distance is therefore 0.8*10 = 8 meaning that point Y' is going to be 8 units away from point Z' or Z.
Subtract 8 from the x coordinate of point Z to get x-8 = 8-8 = 0.
The y coordinate stays the same at y = 4 the whole time.
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In short, point Y starts at (-2,4) and moves to (0,4)
Distance from Y to Z is 10 units
Distance from Y' to Z' is 8 units
8/10 = 4/5 = 0.8 is the scale factor
Point Z does not move. So Z and Z' are at the same location.