Distance, Midpoint and Slope

Front

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

Back

The distance d is given by the formula: 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 using the formula: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the formula for calculating the slope of a line passing through two points (x1, y1) and (x2, y2)?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down.

Front

If the distance between two points is 0, what can be said about those points?

Back

If the distance is 0, the two points are the same point (they have identical coordinates).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other (m1 * m2 = -1).

Front

What is the distance between the points (3, 4) and (3, 10)?

Back

The distance is 6, as the points have the same x-coordinate and the distance is the difference in y-coordinates.

Front

How do you find the coordinates of the midpoint of the segment with endpoints (2, 3) and (4, 7)?

Back

The midpoint is ((2 + 4)/2, (3 + 7)/2) = (3, 5).