Distance, Midpoint and Slope

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

What are the coordinates of the midpoint M between two points (x1, y1) and (x2, y2)?

Back

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2)

Front

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

Back

Slope (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.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

If a line has a slope of m = 5/6, what is the slope of a line that is perpendicular to it?

Back

The slope of the perpendicular line is -6/5.

Front

How do you calculate the distance between the points (-5, -8) and (-1, -16)?

Back

Distance = √((-1 - (-5))² + (-16 - (-8))²) = 8.9.

Front

What are the coordinates of the midpoint of the segment with endpoints (1, -3) and (5, 7)?

Back

Midpoint = ((1 + 5)/2, (-3 + 7)/2) = (3, 2).

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The product of their slopes is -1.

Front

If the slope of a line is 1/1, what does this indicate about the line?

Back

This indicates that the line rises 1 unit for every 1 unit it runs, making a 45-degree angle with the x-axis.