Distance Formula

Front

What is the distance formula used to calculate the distance between two points in a Cartesian plane?

Back

The distance formula is given by d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

How do you find the distance between the points (1, 3) and (5, 6)?

Back

Using the distance formula: d = √((5 - 1)² + (6 - 3)²) = √(16 + 9) = √25 = 5.

Front

What is the distance between the points A(2, 0) and B(-2, 4)?

Back

Using the distance formula: d = √((-2 - 2)² + (4 - 0)²) = √(16 + 16) = √32 = 4√2.

Front

What does the term 'Cartesian plane' refer to?

Back

The Cartesian plane is a two-dimensional coordinate system defined by a horizontal axis (x-axis) and a vertical axis (y-axis), where each point is represented by an ordered pair (x, y).

Front

What is the significance of the distance formula in geometry?

Back

The distance formula is significant in geometry as it allows for the calculation of the straight-line distance between two points, which is essential for solving various geometric problems.

Front

What is the geometric interpretation of the distance formula?

Back

The distance formula represents the length of the hypotenuse of a right triangle formed by the horizontal and vertical distances between two points.

Front

How can the distance formula be applied in real-world scenarios?

Back

The distance formula can be used in various real-world scenarios, such as calculating distances in navigation, architecture, and computer graphics.

Front

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

Back

The distance formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

What is the distance between the points (3, 4) and (3, 8)?

Back

The distance is d = √((3 - 3)² + (8 - 4)²) = √(0 + 16) = √16 = 4.

Front

If the distance between two points is 0, what can be inferred about the points?

Back

If the distance between two points is 0, it means that the two points are the same point, having identical coordinates.