Graph transformations GCSE maths. Please helpppp. Thanks
1 answer:
<h3>Answer: Rotate 180 degrees around point B</h3>
Explanation:
Point A(-3,1) moves to A ' (1,1). The line through these two points is y = 1.
Point C(-3,3) moves to C ' (1, -1). The line through these two points is y = -x
These two lines intersect at point B(-1,1) which is the invariant point, aka fixed point. It is the center of rotation.
Notice how points A, B and A' are collinear (i.e. they are on the same line). The same can be said about points C, B and C'.
Because of these two sets of collinear points, it means we have a 180 degree rotation going on.
Check out the diagram below.
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Answer:
(a)
The probability that you stop at the fifth flip would be
(b)
The expected numbers of flips needed would be
Therefore, suppose that , then the expected number of flips needed would be 1/0.5 = 2.
Step-by-step explanation:
(a)
Case 1
Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be
Case 2
Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be
Therefore the probability that you stop at the fifth flip would be
(b)
The expected numbers of flips needed would be
Therefore, suppose that , then the expected number of flips needed would be 1/0.5 = 2.