2.5 yds
C=2πr
d=2r
Solving ford
d=C
π=7.85
π≈2.
Answer: A. preserves length, angle measures and distance between points
Rigid motions or isometries are any of the three transformations below
- translation (aka shifting)
- rotation
- reflection
Any of those three transformations will keep the figure the same size and shape. That means distances between any two points are kept the same, and angle measures are kept the same as well. Everything is kept the same. The only difference is that the figure is in a different location, is rotated somehow, or it is reflected some way. You can use a series of transformations to undo everything to get the original figure back.
If you wanted to change the size of the figure, then you would apply dilation, which isn't an isometry.
The numbers given in the problem above are part of an arithmetic sequence with first and sixth terms equal to -21 and -36, respectively. Firstly, calculate for the common difference (d).
d = (-36 - -21) / (6 - 1) = -3
The arithmetic mean is calculated by adding -3 to the term prior to it.
a2 = -21 + -3 = -24 a3 = -24 + -3 = -27
a4 = -27 + -3 = -30 a5 = -30 + -3 = -33
Thus the four arithmetic means are -24, -27, -30, and -33.
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Or use photomath, it is also useful!
