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

How do you calculate the perimeter of a rectangle given its vertices?

Back

To calculate the perimeter of a rectangle, use the formula: P = 2(length + width). Length and width can be determined from the coordinates of the vertices.

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

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

Back

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

Front

If a rectangle has vertices at (3, 2), (-2, 2), (-2, -1), and (3, -1), what are its length and width?

Back

Length = 5 units (from x-coordinates) and Width = 3 units (from y-coordinates).

Front

What is the significance of the distance formula in real-world applications?

Back

The distance formula is used in various fields such as navigation, architecture, and computer graphics to determine the distance between points.

Front

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

Back

The midpoint M is calculated as: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the relationship between the coordinates of points on a horizontal line?

Back

Points on a horizontal line have the same y-coordinate.

Front

What is the relationship between the coordinates of points on a vertical line?

Back

Points on a vertical line have the same x-coordinate.

Front

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

Back

Two points are the same if their x-coordinates and y-coordinates are identical.