Reflections Over Axes

Front

What is a reflection in geometry?

Back

A transformation that flips a figure over a line, creating a mirror image.

Front

What is the x-axis?

Back

The horizontal axis in a coordinate plane, where y=0.

Front

What is the y-axis?

Back

The vertical axis in a coordinate plane, where x=0.

Front

How do you reflect a point (x, y) over the x-axis?

Back

Change the sign of the y-coordinate: (x, y) becomes (x, -y).

Front

How do you reflect a point (x, y) over the y-axis?

Back

Change the sign of the x-coordinate: (x, y) becomes (-x, y).

Front

Reflect the point (4, 5) over the x-axis.

Back

(4, -5)

Front

Reflect the point (-3, 2) over the y-axis.

Back

(3, 2)

Front

What is the result of reflecting the point (0, 0) over any axis?

Back

(0, 0) - The origin remains unchanged.

Front

If a point (a, b) is reflected over the x-axis, what is the new point?

Back

(a, -b) - The x-coordinate remains the same, the y-coordinate changes sign.

Front

If a point (a, b) is reflected over the y-axis, what is the new point?

Back

(-a, b) - The y-coordinate remains the same, the x-coordinate changes sign.