Distance (Pythagorean Theorem)

Distance (Pythagorean Theorem)

Assessment

Flashcard

Mathematics

8th Grade

Hard

CCSS
HSG.GPE.B.7, 8.G.B.8, 3.MD.C.7B

+1

Standards-aligned

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

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 is expressed as: c² = a² + b².

Tags

CCSS.8.G.B.8

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).

Tags

CCSS.HSG.GPE.B.7

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.

Tags

CCSS.HSG.GPE.B.7

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).

Tags

CCSS.HSG.GPE.B.7

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.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.HSG.GPE.B.7

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.

Tags

CCSS.HSG.GPE.B.7

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