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

What is the distance between the points (1, -2) and (4, 1)?

Back

Using the distance formula: d = √((4 - 1)² + (1 - (-2))²) = √(3² + 3²) = √(9 + 9) = √18 ≈ 4.2.

Front

If the coordinates of two points are (3, 4) and (0, 0), what is the distance between them?

Back

Using the distance formula: d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the significance of the Pythagorean Theorem in finding distances on a coordinate plane?

Back

The Pythagorean Theorem allows us to calculate the straight-line distance between two points, which is essential in geometry and various applications in real life.

Front

What is the formula for calculating the distance between two points in a 2D plane?

Back

The formula is d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

Using the distance formula: d = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

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

Back

Using the distance formula: d = √((2 - (-1))² + (2 - (-1))²) = √(3² + 3²) = √(9 + 9) = √18 ≈ 4.2.

Front

How do you round the distance to the nearest tenth?

Back

To round to the nearest tenth, look at the hundredths place. If it is 5 or more, round up; if it is less than 5, round down.

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) = √(3² + 4²) = √(9 + 16) = √25 = 5.