Reflections and Distance in the Coordinate Plane

Front

What is a reflection in the coordinate plane?

Back

A reflection in the coordinate plane is a transformation that flips a figure over a line, creating a mirror image.

Front

What happens to the coordinates of a point when it is reflected across the x-axis?

Back

When a point (x, y) is reflected across the x-axis, its coordinates change to (x, -y).

Front

What happens to the coordinates of a point when it is reflected across the y-axis?

Back

When a point (x, y) is reflected across the y-axis, its coordinates change to (-x, y).

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance is calculated using the formula: Distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between the points (3, 4) and (7, 1)?

Back

The distance is 5 units.

Front

What does a reflection over the x-axis look like on a graph?

Back

A reflection over the x-axis flips the figure vertically, keeping the x-coordinates the same and changing the sign of the y-coordinates.

Front

What does a reflection over the y-axis look like on a graph?

Back

A reflection over the y-axis flips the figure horizontally, keeping the y-coordinates the same and changing the sign of the x-coordinates.

Front

If the point (2, 3) is reflected over the y-axis, what are the new coordinates?

Back

The new coordinates are (-2, 3).

Front

If the point (-4, 5) is reflected over the x-axis, what are the new coordinates?

Back

The new coordinates are (-4, -5).

Front

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

Back

The result is still (0, 0) because it is the origin.