Distance, Midpoint, and Slope

Front

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

Calculate the slope of the line that passes through the points (2, 3) and (4, 7).

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

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

Find the distance between the points (1, 2) and (4, 6).

Back

Distance = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the midpoint formula for two points (x1, y1) and (x2, y2)?

Back

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

Front

Calculate the midpoint of the points (2, 3) and (4, 7).

Back

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

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line.

Front

If a line has an undefined slope, what does that indicate about the line?

Back

An undefined slope indicates a vertical line.

Front

What is the perimeter of a triangle with vertices at (0, 0), (3, 0), and (3, 4)?

Back

Perimeter = 3 + 4 + 5 = 12 (using the distance formula for the sides).