Unless otherwise specified we usually assume the dilation is about the origin. That is you can tell the scale factor by the way the distance to the origin changes.
Point C, for example, is 6 units from the origin. Its image, C' is 4 units from the origin. Then the scale factor image/original is 4/6 = 2/3.
Your green question mark gets filled with 3 to make the fraction 2/3.
_____
To find the translation, pick any point on A'B'C' and find the corresponding point A'', B'', or C''. Count the squares you have to go left to get from A' to A'', for example. That will be 5 to the left. Similarly, count the squares you have to go down to get from A' to A''. That will be 4 down.
78
step by step explanation:
first: divide 600 and 15
answer to 600/15: 40
second: divide 3120 and 40
final answer: 78
Groups of four for the group of 288 and groups of five for the group of 360
Answer:
(Assuming you want your answer in radians)
If you want the answer in degrees just multiply your answer in radians by 
giving you:
.
We can do this since 
(half the circumference of the unit circle is equivalent to 180 degree rotation).
Step-by-step explanation:
is going to output an angle measurement in ![[0,\pi]](https://tex.z-dn.net/?f=%5B0%2C%5Cpi%5D)
.
So we are looking to solve the following equation in that interval:
.
This happens in the second quadrant on the given interval.
The solution to the equation is .
So we are saying that 
implies 
since ![\frac{3\pi}{4} \in [0,\pi]](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%5Cin%20%5B0%2C%5Cpi%5D)
.
Answer is .
