If the midpoint of a line segment is (3, 5) and one endpoint is (1, 2), what is the other endpoint?

Let the other endpoint be (x, y). Using the midpoint formula: $$(3, 5) = \\left(\\frac{1 + x}{2}, \\frac{2 + y}{2}\\right)$$ . Solving gives (5, 8).

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

Using the distance formula: $$d = \\sqrt{(2 - (-1))^2 + (2 - (-1))^2} = \\sqrt{9 + 9} = 3\\sqrt{2}$$ .

How do you derive the distance formula 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 (4, 3) and (0, 6)?

Using the distance formula: $$d = \\sqrt{(0 - 4)^2 + (6 - 3)^2} = \\sqrt{16 + 9} = 5$$ .

What is the midpoint of the points (1, 2) and (3, 4)?

Using the midpoint formula: $$M = \\left(\\frac{1 + 3}{2}, \\frac{2 + 4}{2}\\right) = (2, 3)$$ .

If the distance between two points is 10 and one point is (0, 0), what could be the coordinates of the other point?

Possible coordinates could be (10, 0), (0, 10), (-10, 0), or (0, -10), among others.

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

The distance formula in 3D is given by $$d = \\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 + (z_{2} - z_{1})^2}$$ .

What is the relationship between the distance formula and the coordinate plane?

The distance formula allows us to measure the straight-line distance between any two points in the Cartesian coordinate plane.

Midpoint and Distance Formulas Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the distance formula?

Back

2.

FLASHCARD QUESTION

Front

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

Back

3.

FLASHCARD QUESTION

Front

How do you find the midpoint of the points (2, 4) and (6, 8)?

Back

4.

FLASHCARD QUESTION

Front

Calculate the distance between the points (1, 1) and (4, 5).

Back

5.

FLASHCARD QUESTION

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

6.

FLASHCARD QUESTION

Front

Find the distance between the points (2, 3) and (2, 7).

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the distance formula in geometry?

Back

The distance formula calculates the length of a line segment between two points in a coordinate plane.

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