Distance on Coordinate Plane: Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

How do you find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane?

Back

The distance d can be found using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

Calculate the distance between the points (3, 4) and (0, 0).

Back

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

Front

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

Back

Using the distance formula: d = √((1 - (-5))² + (-2 - 5)²) = √((1 + 5)² + (-7)²) = √(6² + 7²) = √(36 + 49) = √85 ≈ 9.2.

Front

If point A is at (2, 3) and point B is at (2, 7), what is the distance between them?

Back

The distance is |7 - 3| = 4.

Front

What is the distance between the points (1, 1) and (4, 5)?

Back

Using the distance formula: d = √((4 - 1)² + (5 - 1)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

Find the distance between points (0, 0) and (6, 8).

Back

Using the distance formula: d = √((6 - 0)² + (8 - 0)²) = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is the distance between the points (3, 2) and (3, -1)?

Back

The distance is |2 - (-1)| = |2 + 1| = 3.

Front

If point C is at (-3, -4) and point D is at (1, 2), what is the distance between them?

Back

Using the distance formula: d = √((1 - (-3))² + (2 - (-4))²) = √((1 + 3)² + (2 + 4)²) = √(4² + 6²) = √(16 + 36) = √52 ≈ 7.2.

Front

What is the distance between points (5, 5) and (5, 10)?

Back

The distance is |10 - 5| = 5.