Distance on the Coordinate Plane

Front

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

Back

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

Front

What does an ordered pair represent in the coordinate plane?

Back

An ordered pair (x, y) represents a point in the coordinate plane, where 'x' is the horizontal position and 'y' is the vertical position.

Front

How do you determine the length of a side of a rectangle given its vertices on the coordinate plane?

Back

To find the length of a side, calculate the distance between the coordinates of the two endpoints of that side using the distance formula.

Front

What is the significance of the x-axis and y-axis in the coordinate plane?

Back

The x-axis is the horizontal line, and the y-axis is the vertical line. They intersect at the origin (0, 0) and help define the position of 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 distance between the points (2, 3) and (5, 7)?

Back

Using the distance formula: d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Front

If point A is at (1, 2) and point B is at (4, 6), what is the distance between them?

Back

The distance is d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

Front

What is the definition of a rectangle in the context of the coordinate plane?

Back

A rectangle is a quadrilateral with opposite sides equal and all angles right angles, defined by its vertices on the coordinate plane.

Front

How do you write the coordinates of a point that is 3 units east and 1 unit south of the origin?

Back

Starting from the origin (0, 0), moving 3 units east and 1 unit south gives the point (3, -1).

Front

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

Back

Points on the same vertical line have the same x-coordinate but different y-coordinates.