Reflections and Distance in the Coordinate plane

Front

What is the formula to calculate the distance between two points (x1, y1) and (x2, y2) in the coordinate plane?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between the points (0, 6) and (0, -4)?

Back

10 units.

Front

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

Back

To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate: the reflected point is (-x, y).

Front

What is the reflection of the point D (4, 3) over the y-axis?

Back

D' (-4, 3).

Front

What is the distance between the points (-3, 4) and (-3, -8)?

Back

12 units.

Front

What is the reflection of the point B (-7, -8) over the y-axis?

Back

B' (7, -8).

Front

What is the significance of the y-axis in reflections?

Back

The y-axis serves as a mirror line for reflections; points on the left of the y-axis will have their x-coordinates negated when reflected.

Front

If a point is reflected over the x-axis, what happens to its coordinates?

Back

The y-coordinate changes sign: the reflected point (x, y) becomes (x, -y).

Front

What is the distance between two points with the same x-coordinate?

Back

The distance is the absolute difference between their y-coordinates.

Front

How do you find the distance between two points with the same y-coordinate?

Back

The distance is the absolute difference between their x-coordinates.