The second one 2(2x) +2(4x+3)
Answer:
or 1.5
Step-by-step explanation:
Now we know it's a dilation. So we can use any two points. I chose V and V'.
V: (3,6)
V': (2,4)
So how we get from 6 to 4?

You can tell it's 1.5 aswell because 4 times 1 is 4 and 4 times 0.5 is 2. Add them to get 6.
Therefore, the dilation factor is 1.5.
This revolves around exact trig values - no easy way to say this, you just need to memorise them. They are there for sin cos and tan, but I will give you the main tan ones below - note this is RADIANS (always work in them when you can, everything is better):
tan0: 0
tanpi/6: 1/sqrt(3)
tanpi/4: 1
tanpi/3: sqrt(3)
tanpi/2: undefined
Now we just need to equate -2pi/3 to something we understand. 2pi/3 is 1/3 of the way round a circle, so -2pi/3 is 1/3 of the way round the circle going backwards (anticlockwise), so on a diagram we already know it's in the third quadrant of the circle (somewhere between pi and 3pi/2 rads).
We also know it is pi/3 away from pi, so we are looking at sqrt(3) or -sqrt(3) because of those exact values.
Now we just need to work out if it's positive or negative. You can look up a graph of tan and it'll show that the graph intercepts y at (0,0) and has a period of pi rads. Therefore between pi and 3pi/2 rads, the values of tan are positive. Therefore, this gives us our answer of sqrt(3).
Answer:
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