Endpoints, -Slope, Distance, Midpoint

Front

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

Back

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

Front

Calculate the slope of the line that passes through the points (2, 4) and (6, 12).

Back

Slope = (12 - 4) / (6 - 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 (-5, -8) and (-1, -16).

Back

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

Front

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

Back

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

Front

Find the midpoint of the segment with endpoints (6, 7) and (6, -5).

Back

Midpoint = ((6 + 6)/2, (7 + (-5))/2) = (6, 1)

Front

What is an endpoint in geometry?

Back

An endpoint is a point at one end of a line segment or the starting point of a ray.

Front

Given the endpoint (-4, 5) and midpoint (7, -9), find the other endpoint.

Back

Other endpoint = (2 * midpoint - endpoint) = (2 * (7, -9) - (-4, 5)) = (18, 13)

Front

What does the term 'slope' represent in a linear equation?

Back

Slope represents the rate of change of y with respect to x, indicating the steepness of the line.

Front

Calculate the distance between the points (-4, 5) and (7, 18).

Back

Distance = √((7 - (-4))² + (18 - 5)²) = 17.03