Distance, Midpoint, and Slope

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

What is the definition of the midpoint of a line segment?

Back

The midpoint is the point that divides the segment into two equal parts, calculated as ((x1 + x2)/2, (y1 + y2)/2).

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What is the distance between the points (3, 4) and (7, 1)?

Back

Distance = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Front

What is the midpoint of the points (2, 3) and (4, 7)?

Back

Midpoint = ((2 + 4)/2, (3 + 7)/2) = (3, 5)

Front

If a line passes through the points (1, 2) and (3, 6), what is its slope?

Back

Slope = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the distance between the points (0, 0) and (6, 8)?

Back

Distance = √((6 - 0)² + (8 - 0)²) = √(36 + 64) = √100 = 10.

Front

What is the formula for the slope-intercept form of a line?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness of a line, calculated as the rise over run.

Front

Find the midpoint of the segment with endpoints (5, 5) and (1, 1).

Back

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