Pythagorean Theorem, Distance, and Midpoint

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

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

Back

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

Tags

CCSS.HSG.GPE.B.7

Front

What is the midpoint formula?

Back

The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula: M = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

Find the endpoint of the segment with endpoint (3, -2) and midpoint (5, 4).

Back

(7, 10)

Tags

CCSS.HSG.GPE.B.6

Front

Find the endpoint of the segment with endpoint (-4, 5) and midpoint (7, -9).

Back

(18, 13)

Tags

CCSS.HSG.GPE.B.6

Front

What is the length of the missing side if one side is 5 cm and the hypotenuse is 13 cm?

Back

12 cm (using Pythagorean Theorem: 5² + b² = 13²).

Tags

CCSS.8.G.B.8

Front

Find the length of the missing side if one side is 60 in. and the hypotenuse is 80 in.

Back

80 in.

Tags

CCSS.8.G.B.7

Front

How do you calculate the length of a side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Tags

CCSS.8.G.B.8

Front

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

Back

5 units (using the distance formula: d = √((5-2)² + (7-3)²) = √(9 + 16) = √25 = 5).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

5 units (using the distance formula: d = √((4-1)² + (5-1)²) = √(9 + 16) = √25 = 5).

Tags

CCSS.HSG.GPE.B.7