Pythagorean Theorem and Distance Formula

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: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the Distance Formula?

Back

The Distance Formula is used to determine the distance between two points (x1, y1) and (x2, y2) in a coordinate plane. It is given by: Distance = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

Distance = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What is the ordered pair for point B if it is located at 5 units right and 3 units up from the origin?

Back

The ordered pair for point B is (5, 3).

Tags

CCSS.5.G.A.2

Front

If a triangle has sides of lengths 3 and 4, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.8

Front

What is the square root of 16?

Back

The square root of 16 is 4.

Tags

CCSS.8.EE.A.2

Front

Find the distance between the points (-1, -1) and (2, 3).

Back

Distance = √((2 - (-1))² + (3 - (-1))²) = √((2 + 1)² + (3 + 1)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

What is the opposite operation of squaring a number?

Back

The opposite operation of squaring a number is taking the square root.

Tags

CCSS.8.EE.A.2

Front

What is the distance between the points (1, 2) and (5, 4)?

Back

Distance = √((5 - 1)² + (4 - 2)²) = √(4 + 4) = √8 = 2√2 ≈ 4.5.

Tags

CCSS.HSG.GPE.B.7

Front

If point C is at (0, 0) and point D is at (3, 4), what is the distance between them?

Back

Distance = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7