Parallel Lines and Distance Formula

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet. They are always the same distance apart and have the same slope.

Front

What is the distance formula?

Back

The distance formula is used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: d = √((x2 - x1)² + (y2 - y1)²).

Front

Calculate the distance between the points (3, 4) and (7, 1).

Back

The distance is 5 units.

Front

What is the slope of parallel lines?

Back

The slope of parallel lines is the same; if two lines are parallel, they have identical slopes.

Front

Find the distance between the points (-12, 1) and (12, -1).

Back

The distance is 24.08.

Front

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

Back

The distance is 17.03.

Front

What is the significance of the distance formula in geometry?

Back

The distance formula helps determine how far apart two points are in a coordinate system, which is essential for solving various geometric problems.

Front

If two lines are parallel, what can be said about their equations?

Back

The equations of parallel lines will have the same slope but different y-intercepts.

Front

Calculate the distance between the points (-5, -8) and (-1, -16).

Back

The distance is 8.9.

Front

What is the relationship between the distance formula and the Pythagorean theorem?

Back

The distance formula is derived from the Pythagorean theorem, as it calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates.