Question

20 Points, Please explain answer.

Lia claims that a reflection over the y-axis will always carry a circle drawn on the coordinate plane to a circle with the same center and the same radius. Which statement best describes Lia's claim?

A
Lia is correct as a reflected circle will always have the same center and always have the same radius as the original circle.

B
Lia is incorrect as a reflected circle will not always have the same radius and will not always have the same center as the original circle.

C
Lia is correct in stating that the reflected circle will always have the same radius, but is incorrect in stating that the reflected circle will always have the same center.

D
Lia is incorrect in stating that the reflected circle will always have the same radius, but is correct in stating that the reflected circle will always have the same center.

Answer 1

C. Lia is correct in stating that the reflected circle will always have the same radius, but is incorrect in stating that the reflected circle will always have the same center.

Explanation:

Lia's claim is not correct, because when we reflect a figure, its coordinates variate. In this case, Lisa is trying to reflect a circle over the y-axis, which will change y-axis coordinates. The center of the circle is gonna change its y-axis coordinate, for example, if the center is
`C(2;3)`, its reflection will be
`C(2;-3)`

Therefore, the center of the circle will not remain the same. However, the radius will be the same, because changing y-axis coordinates don't affect the distance between the center and the circumference of the circle.

So, the correct answer is option C.

Answer 2

Answer: YOUR ANSWER WOULD BE B

Step-by-step explanation: Your answer would be B because when you reflect something on the y-axis it always goes one cube or dashed line forward so it will not have the same radius nor the circle hope this helps you alot