I'll do the first two problems to get you started
Answers:
1a) The scale factor is 61b) See figure 1 below2a) scale factor = 5/2 = 2.52b) Center of dilation = (-7,0)2c) Point E' is at (-12,0)2d) See figure 2 below
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Explanation for problem 1, part (a)
Measure out the horizontal piece of the smaller letter "A"
Let's say it's 1 unit.
Then measure the same corresponding part of the larger "A" and you should note that it's 6 units across. Therefore, the scale factor is 6.
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Explanation for problem 1, part (b)
Refer to figure 1 below. The image (in blue) is smaller than the preimage this time. Note the red markings to show the scale factor is 6 for the previous part (a).
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Explanation for problem 2, part (a)
Let point A be the center of dilation, which in this case is (-7,0).
The distance from A to C is 2 units
The distance from A to C' is 5 units
The scale factor is therefore (AC')/(AC) = 5/2 = 2.5
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Explanation for problem 2, part (b)
The center of dilation is where everything expands or shrinks from. Think of it like the center of the universe so to speak.
In this case, such a specified point is (-7,0). This point does not move while every other point does move.
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Explanation for problem 2, part (c)
Notice the gap from C to C' is 3 units. This is the same from E to E'
E(-9,0) moves 3 units to the left to arrive at E'(-12,0).
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Explanation for problem 2, part (d)
Refer to figure 2.
The distance from B' to D' is 20 units. Half of which is 10 units. So we move 10 units from from B'(-7,10) to arrive at (-7,0). Point D'' is at (-7,0) which is the exact same location as point A. The other points C' and E' will move in a similar fashion. The goal is to have them be half as close compared to before.
Note that B' does not move, so B' and B'' occupy the same location (-7,10).
