Distance Between Points on the Coordinate Plane

Front

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

Back

The distance d is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What does the distance formula derive from in geometry?

Back

The distance formula is derived from the Pythagorean theorem.

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

The distance is 5, calculated using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Front

How do you find the distance between points with negative coordinates, such as (-2, -3) and (1, 1)?

Back

Use the distance formula: d = √((1 - (-2))² + (1 - (-3))²) = √((1 + 2)² + (1 + 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the distance between the points (1, 1) and (4, 5)?

Back

The distance is √41, calculated using the distance formula: d = √((4 - 1)² + (5 - 1)²) = √(3² + 4²) = √(9 + 16) = √25 = √41.

Front

If the distance between two points is 10 units, what could be the possible coordinates of these points if one point is (0, 0)?

Back

Possible coordinates could be (10, 0), (0, 10), (-10, 0), (0, -10), or any point that satisfies the distance formula with (0, 0).

Front

What is the significance of the square root in the distance formula?

Back

The square root is used to ensure that the distance is a non-negative value, as distance cannot be negative.

Front

How can you determine if two points are the same using the distance formula?

Back

If the distance calculated using the distance formula is 0, then the two points are the same.

Front

What is the distance between the points (-1, -1) and (2, 3)?

Back

The distance is 5, calculated as d = √((2 - (-1))² + (3 - (-1))²) = √((2 + 1)² + (3 + 1)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

The distance is 5, calculated as d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.