Pythagorean Theorem on the Coordinate Plane

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 the coordinate plane?

Back

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

Front

What is the length of the hypotenuse in a right triangle with legs of length 3 and 4?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

If a right triangle has one leg measuring 6 units and the hypotenuse measuring 10 units, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b²; 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8.

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What does the y-axis represent on the coordinate plane?

Back

The y-axis represents the vertical line on the coordinate plane where x = 0.

Front

What does the x-axis represent on the coordinate plane?

Back

The x-axis represents the horizontal line on the coordinate plane where y = 0.

Front

How do you determine if a triangle is a right triangle using coordinates?

Back

Check if the squares of the lengths of the two shorter sides add up to the square of the longest side using the distance formula.

Front

What is the distance between the points (2, 3) and (2, 7)?

Back

Using the distance formula: d = √((2 - 2)² + (7 - 3)²) = √(0 + 16) = √16 = 4.

Front

If point A is at (3, 4) and point B is at (3, 10), what is the distance between them?

Back

The distance is the difference in the y-coordinates: |10 - 4| = 6.