Question

Plz help is the statements true or false

Answer 1

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.