Distance and Reflections in the Coordinate Plane Flashcard

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 (3, 4) and (3, -2)?

Back

The distance is 6 units.

Front

How do you find the coordinates of the midpoint between two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the distance between the points (5, 5) and (5, 5)?

Back

The distance is 0 units.

Front

What does it mean for two points to be reflections across the x-axis?

Back

If point A is (x, y), its reflection across the x-axis is (x, -y).

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

The distance is 5 units.

Front

How do you determine if two points are the same in the coordinate plane?

Back

Two points are the same if their coordinates are identical, i.e., (x1, y1) = (x2, y2).

Front

What is the distance between the points (0, 0) and (0, 10)?

Back

The distance is 10 units.

Front

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

Back

The x-axis serves as a line of symmetry; points above it reflect to points below it and vice versa.

Front

How do you calculate the distance between points (2, 3) and (2, -1)?

Back

The distance is 4 units.