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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

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

Back

Use the distance formula: Distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the square root of a number?

Back

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3.

Front

If the lengths of the two legs of a right triangle are 3 units and 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

Front

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

Back

Distance = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

Front

What does it mean to square a number?

Back

To square a number means to multiply the number by itself. For example, 3 squared (3²) is 3 x 3 = 9.

Front

What is the distance between the points (2, 3) and (5, 7)?

Back

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

Front

What is the formula for calculating the distance between two points?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.