Distance on a Coordinate Plane

Front

What is the distance formula on a coordinate plane?

Back

The distance between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you find the midpoint between two points on a coordinate plane?

Back

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

Front

What is the definition of a coordinate plane?

Back

A coordinate plane is a two-dimensional surface formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis).

Front

What are the four quadrants of a coordinate plane?

Back

The four quadrants are: Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), Quadrant IV (x > 0, y < 0).

Front

How do you determine the distance between points (3, 4) and (7, 1)?

Back

Using the distance formula: d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Front

What is the significance of the origin in a coordinate plane?

Back

The origin is the point (0, 0) where the x-axis and y-axis intersect, serving as the reference point for all other points.

Front

How do you plot a point on a coordinate plane?

Back

To plot a point (x, y), start at the origin, move x units along the x-axis, and then y units up (if y is positive) or down (if y is negative).

Front

What is the formula for calculating the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated as: m = (y2 - y1) / (x2 - x1).

Front

How do you find the distance between points (-2, 3) and (4, -1)?

Back

Using the distance formula: d = √((4 - (-2))² + (-1 - 3)²) = √(36 + 16) = √52 = 2√13.

Front

What is the definition of a line segment in geometry?

Back

A line segment is a part of a line that is bounded by two distinct endpoints.