Distance and Midpoint/Parallel/Perp

Front

What is the formula to find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

Calculate the midpoint of the endpoints (2, 4) and (6, 8).

Back

The midpoint is (4, 6).

Front

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

Back

Front

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

Back

Front

If the midpoint is (3, 5) and one endpoint is (1, 2), how do you find the other endpoint?

Back

Use the formula: other endpoint = (2 * midpoint - endpoint). So, it is (5, 8).

Front

What does it mean for two lines to be parallel in a coordinate plane?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular in a coordinate plane?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

Find the coordinates of the other endpoint if the midpoint is (4, 3) and one endpoint is (2, 1).

Back

The other endpoint is (6, 5).

Front

What is the slope of a line that passes through the points (2, 3) and (4, 7)?

Back

The slope m is given by m = (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2.

Front

If a line has a slope of 3, what is the slope of a line perpendicular to it?

Back

The slope of the perpendicular line is -1/3.