What is the Pythagorean Theorem?
Distance (Pythagorean Theorem)

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Mathematics
•
8th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
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 is expressed as: c² = a² + b².
2.
FLASHCARD QUESTION
Front
How do you calculate the distance between two points in a coordinate plane?
Back
The distance d between two points (x1, y1) and (x2, y2) can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).
3.
FLASHCARD QUESTION
Front
What is the distance formula derived from?
Back
The distance formula is derived from the Pythagorean Theorem, where the distance between two points forms the hypotenuse of a right triangle.
4.
FLASHCARD QUESTION
Front
What is the length of the diagonal of a rectangle with vertices at (x1, y1), (x2, y1), (x2, y2), and (x1, y2)?
Back
The length of the diagonal can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).
5.
FLASHCARD QUESTION
Front
If a rectangle has a width of 6 units and a height of 8 units, what is the length of its diagonal?
Back
Using the Pythagorean Theorem, the diagonal d = √(6² + 8²) = √(36 + 64) = √100 = 10 units.
6.
FLASHCARD QUESTION
Front
What is the significance of the coordinates (-6, -4) and (1, 3) in calculating distance?
Back
These coordinates represent two points in a Cartesian plane, and their distance can be calculated using the distance formula.
7.
FLASHCARD QUESTION
Front
How do you find the distance between points (2, 4) and (2, -4)?
Back
Using the distance formula: d = √((2 - 2)² + (-4 - 4)²) = √(0 + 64) = √64 = 8 units.
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