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 A(3,1) and B(-2,-1)?

Back

Using the distance formula: d = √((-2 - 3)² + (-1 - 1)²) = √((-5)² + (-2)²) = √(25 + 4) = √29 ≈ 5.39.

Front

What is the distance between the points (-5, -8) and (-1, -16)?

Back

Using the distance formula: d = √((-1 - (-5))² + (-16 - (-8))²) = √((4)² + (-8)²) = √(16 + 64) = √80 ≈ 8.94.

Front

How do you express the distance between points A(2,0) and B(-2,4) using the distance formula?

Back

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

Front

What is the significance of the distance formula in geometry?

Back

The distance formula is significant as it allows us to calculate the straight-line distance between two points in a plane, which is fundamental in geometry, physics, and various applications.

Front

What are the coordinates of point A in the distance formula?

Back

Point A is represented as (x1, y1) in the distance formula.

Front

What are the coordinates of point B in the distance formula?

Back

Point B is represented as (x2, y2) in the distance formula.

Front

What does the variable 'd' represent in the distance formula?

Back

The variable 'd' represents the distance between the two points.

Front

How can the distance formula be derived from the Pythagorean theorem?

Back

The distance formula can be derived from the Pythagorean theorem by considering the distance as the hypotenuse of a right triangle formed by the differences in x and y coordinates.

Front

What is the distance between the points (0,0) and (x,y)?

Back

The distance is given by d = √(x² + y²).