How do you find the distance between the points (-1, -1) and (3, 3)?

Using the distance formula: $$d = \\sqrt{(3 - (-1))^2 + (3 - (-1))^2} = \\sqrt{16 + 16} = \\sqrt{32} = 4\\sqrt{2}$$ .

What is the formula for calculating the distance between two points in a 3D space?

The distance formula in 3D is: $$d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$$ .

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

Using the distance formula: $$d = \\sqrt{(6 - 0)^2 + (8 - 0)^2} = \\sqrt{36 + 64} = \\sqrt{100} = 10$$ .

What does the midpoint represent in a geometric context?

The midpoint represents the point that is exactly halfway between two points on a line segment.

If the coordinates of two points are (5, 5) and (5, 10), what is the midpoint?

The midpoint is $$M = \\left(\\frac{5 + 5}{2}, \\frac{5 + 10}{2}\\right) = (5, 7.5)$$ .

How can the distance formula be derived from the Pythagorean theorem?

The distance formula is derived by applying the Pythagorean theorem to the right triangle formed by the horizontal and vertical distances between two points.

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

The distance is $$d = \\sqrt{(1 - 1)^2 + (-1 - 1)^2} = \\sqrt{0 + 4} = 2$$ .

What is the formula for the distance between two points in a coordinate plane?

The formula is: $$d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

Mrs. Kim's Distance and Midpoint Formulas Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the distance formula used to find the distance between two points (x1, y1) and (x2, y2)?

Back

Tags

CCSS.HSG.GPE.B.7

2.

FLASHCARD QUESTION

Front

What is the midpoint formula for finding the midpoint between two points (x1, y1) and (x2, y2)?

Back

Tags

CCSS.HSG.GPE.B.6

3.

FLASHCARD QUESTION

Front

How do you calculate the distance between the points (3, 0) and (5, -2)?

Back

Tags

CCSS.HSG.GPE.B.7

4.

FLASHCARD QUESTION

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Tags

CCSS.HSG.GPE.B.7

5.

FLASHCARD QUESTION

Front

What is the significance of the distance formula in geometry?

Back

The distance formula is used to determine the length of a line segment between two points in a coordinate plane.

Tags

CCSS.HSG.GPE.B.7

6.

FLASHCARD QUESTION

Front

If the coordinates of two points are (2, 3) and (2, 7), what is the distance between them?

Back

Tags

CCSS.HSG.GPE.B.7

7.

FLASHCARD QUESTION

Front

What is the midpoint of the points (2, 3) and (4, 7)?

Back

Tags

CCSS.HSG.GPE.B.6

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