Distance Formula

Front

What is the Distance Formula?

Back

The Distance Formula is used to determine the distance between two points in a coordinate plane. It is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What do the variables in the Distance Formula represent?

Back

In the Distance Formula d = √((x2 - x1)² + (y2 - y1)²), (x1, y1) and (x2, y2) are the coordinates of the two points, and d represents the distance between them.

Front

Calculate the distance between the points (2, 3) and (5, 7).

Back

d = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

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

Back

d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

Find the distance between the points (-1, -1) and (2, 2).

Back

d = √((2 - (-1))² + (2 - (-1))²) = √(3² + 3²) = √(9 + 9) = √18 = 3√2.

Front

What is the distance between the points (1, 2) and (1, 5)?

Back

d = √((1 - 1)² + (5 - 2)²) = √(0 + 3²) = √9 = 3.

Front

How does the Distance Formula relate to 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.

Front

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

Back

d = √((4 - 4)² + (4 - 4)²) = √(0 + 0) = √0 = 0.

Front

Find the distance between the points (3, 3) and (6, 7).

Back

d = √((6 - 3)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

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

Back

d = √((3 - 8)² + (-4 - 8)²) = √((-5)² + (-12)²) = √(25 + 144) = √169 = 13.