Answers:
1. This question is asking for the dilation, or division of each point by a factor of 3. This is shown in the results below:
A' = (-4/3, -2/3)
B' = (1/3, -1)
C' = (2/3, -5/3)
D' = (-1/3, 7/3)
2. This question is asking the same thing as the previous question except for new points and a new scale factor. The results are shown below:
A' = (3, 1)
B' = (-2, -2)
C' = (-4, 6)
D' = (1, -4)
3. This question is basically asking to multiply the area of the fence by two as shown with "extend the fence's range by a scale factor of 2." The results are shown below:
A' = (4, 6)
B' = (-6, 4)
C' = (4, -4)
4. This question is asking for the ratio of each side. Moreover, this means that the same side on both triangles must equal the same ratio. This is shown below:
75/24 = 25/8
60/18 = 10/3
The values of 25/8 and 10/3 are not the same, meaning that the scale ratio is not the same. These two triangles are NOT similar because of this.
5. This question is asking the same thing as question 4. The results are shown below:
10/5 = 2
10/5 = 2
As these values are the same, these two triangles ARE similar because of how the larger triangle is multiplied by a scale factor of 2.
