Finding the Distance Between two Points

Front

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

Back

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

Front

How do you find the distance between the points (5, 0) and (1, 0)?

Back

Using the distance formula: d = √((1 - 5)² + (0 - 0)²) = √(16) = 4.

Front

What is the distance between the points (-11, 1) and (11, -1)?

Back

Using the distance formula: d = √((11 - (-11))² + (-1 - 1)²) = √(22² + (-2)²) = √(484 + 4) = √488 ≈ 22.36.

Front

What does the distance formula represent in geometry?

Back

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

Front

If the coordinates of a point are (4, -6), which letter corresponds to this point in a given mapping?

Back

In the provided mapping, the letter corresponding to the coordinate (4, -6) is Z.

Front

What is the significance of the distance between two points in real-world applications?

Back

The distance between two points can represent physical distances in navigation, architecture, and various fields of science and engineering.

Front

How can you determine if two points are the same using their coordinates?

Back

Two points are the same if their coordinates are identical, meaning (x1, y1) = (x2, y2).

Front

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

Back

Using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Front

What is the geometric interpretation of the distance formula?

Back

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

Front

How do you find the midpoint between two points (x1, y1) and (x2, y2)?

Back

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