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).

Front

How do you find 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 = 5.66.

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 variable 'd' represent in the distance formula?

Back

In the distance formula, 'd' represents the distance between two points in a Cartesian coordinate system.

Front

What are the coordinates of point A in the example A(2,0)?

Back

The coordinates of point A are (2, 0), where 2 is the x-coordinate and 0 is the y-coordinate.

Front

What are the coordinates of point B in the example B(-2,4)?

Back

The coordinates of point B are (-2, 4), where -2 is the x-coordinate and 4 is the y-coordinate.

Front

What is the first step in using the distance formula?

Back

The first step is to identify the coordinates of the two points you are calculating the distance between.

Front

How do you square a number in the context of the distance formula?

Back

To square a number, you multiply the number by itself. For example, (x2 - x1)² means (x2 - x1) * (x2 - x1).

Front

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

Back

The square root in the distance formula ensures that the distance is a non-negative value, as distance cannot be negative.

Front

Can the distance formula be used in three-dimensional space?

Back

Yes, the distance formula can be extended to three dimensions as d = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²).