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.

Tags

CCSS.8.G.B.8

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).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

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

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

Using the distance formula: d = √((1 - (-5))² + (-2 - 5)²) = √(6² + (-7)²) = √(36 + 49) = √85 ≈ 9.2.

Tags

CCSS.HSG.GPE.B.7

Front

Find the distance between the points (5, 3) and (4, 2).

Back

Using the distance formula: d = √((4 - 5)² + (2 - 3)²) = √((-1)² + (-1)²) = √(1 + 1) = √2 ≈ 1.4.

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

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

Tags

CCSS.HSG.GPE.B.7

Front

If the distance between points A(1, 1) and B(x, y) is 10, what is the equation?

Back

The equation is: √((x - 1)² + (y - 1)²) = 10. Squaring both sides gives (x - 1)² + (y - 1)² = 100.

Tags

CCSS.HSG.GPE.A.1

Front

What is the distance between the points (0, 0) and (8, 6)?

Back

Using the distance formula: d = √((8 - 0)² + (6 - 0)²) = √(8² + 6²) = √(64 + 36) = √100 = 10.

Tags

CCSS.HSG.GPE.B.7

Front

Calculate the distance between points J(2, 3) and K(10, 7).

Back

Using the distance formula: d = √((10 - 2)² + (7 - 3)²) = √(8² + 4²) = √(64 + 16) = √80 ≈ 8.2.

Tags

CCSS.HSG.GPE.B.7

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.

Tags

CCSS.HSG.GPE.B.7