Distance and Midpoint on the Coordinate Plane

Front

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

Back

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

Front

How do you find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

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

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts and is equidistant from both endpoints.

Front

If the coordinates of one endpoint of a segment are (x1, y1) and the midpoint is (xm, ym), how can you find the coordinates of the other endpoint (x2, y2)?

Back

Use the formulas: x2 = 2*xm - x1 and y2 = 2*ym - y1.

Front

What is the formula for calculating the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope is calculated as: m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope.

Front

What is the distance between the points (3, 4) and (3, -2)?

Back

The distance is 6, calculated using the distance formula: d = √((3 - 3)² + (-2 - 4)²) = √(0 + 36) = 6.

Front

How do you determine if a slope is positive, negative, or zero?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and a zero slope is horizontal.

Front

What is the distance between the points (-5, 2) and (1, -3)?

Back

The distance is √61, calculated using the distance formula.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other.