Answers:
- (a) True
- (b) True
- (c) False
- (d) True
- (e) False
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Explanations:
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Part (a)
Applying a rotation will not change the length of XY. This means segment X'Y is the same length as segment XY.
Put another way: (distance from X to Y) = (distance from X' to Y)
So if we have Y as the center of the circle, and XY as the radius, then X and X' are both on the same circle.
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Part (b)
As explained in part (a), the segments XY and X'Y are both radii of the same circle, so they are equal to one another.
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Part (c)
Draw a right triangle with side lengths XY, X'Y and hypotenuse XX'
Note how a 45-45-90 triangle forms. We can use the pythagorean theorem to show that XX' is larger than XY. Therefore, XX' and XY aren't equal.
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Part (d)
This angle forms because we rotated point X 90 degrees with the center point as Y. It might help to think of point Y at the origin. So that's why this statement is true.
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Part (e)
This is false because segment X'Y or YX' is a radius and not a diameter. We would need to multiply by 2 to get a diameter.