8.GSR.8.3 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 on a coordinate plane?

Back

To find the distance between two points (x1, y1) and (x2, y2), use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

The distance is 5, calculated using the formula: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Front

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

Back

The distance is approximately 3.61, calculated as: d = √((2 - (-1))² + (3 - (-1))²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

If the coordinates of point A are (x1, y1) and point B are (x2, y2), what does (x2 - x1) represent?

Back

It represents the horizontal distance between the two points.

Front

If the coordinates of point A are (x1, y1) and point B are (x2, y2), what does (y2 - y1) represent?

Back

It represents the vertical distance between the two points.

Front

What is the distance between the points (5, 3) and (4, 2)?

Back

The distance is 1.4, calculated as: d = √((4 - 5)² + (2 - 3)²) = √(1 + 1) = √2 ≈ 1.4.

Front

What is the distance between the points (-9, -1) and (-2, -6)?

Back

The distance is approximately 8.6, calculated as: d = √((-2 - (-9))² + (-6 - (-1))²) = √(7² + (-5)²) = √(49 + 25) = √74 ≈ 8.6.

Front

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

Back

The distance is approximately 9.2, calculated as: d = √((1 - (-5))² + (-2 - 5)²) = √(6² + (-7)²) = √(36 + 49) = √85 ≈ 9.2.

Front

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

Back

The distance is 5, calculated as: d = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.