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 significance of the distance formula in geometry?

Back

The distance formula is used to determine the length of a line segment between two points in a plane, which is fundamental in geometry.

Front

If A(2,0) and B(-2,4), how is the distance between them expressed mathematically?

Back

The distance is expressed as d = √((-2 - 2)² + (4 - 0)²) = √(16 + 16) = √32.

Front

What is the distance between the points (3, 24) and (7, 56)?

Back

Using the distance formula: d = √((7 - 3)² + (56 - 24)²) = √(16 + 1024) = √1040 ≈ 32.2.

Front

What does the term 'Cartesian plane' refer to?

Back

The Cartesian plane is a two-dimensional plane 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 geometric interpretation of the distance formula?

Back

The distance formula represents the length of the straight line connecting two points in a two-dimensional space.

Front

How can the distance formula be derived from 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 (distance) is equal to the sum of the squares of the other two sides (differences in x and y coordinates).

Front

What is the distance between two points if they have the same x-coordinate?

Back

If two points have the same x-coordinate, the distance between them is the absolute difference of their y-coordinates: d = |y2 - y1|.

Front

What is the distance between two points if they have the same y-coordinate?

Back

If two points have the same y-coordinate, the distance between them is the absolute difference of their x-coordinates: d = |x2 - x1|.