What is the distance between the points (-4, 5) and (7, y) if the distance is $$\sqrt{290}$$ ?

Using the distance formula: $$\sqrt{(7 - (-4))^2 + (y - 5)^2} = \sqrt{290}$$ . Solving gives y = 18.

If the distance between point A(2,9) and point B(5,y) is $$\sqrt{34}$$ , what is the value of y if y > 9?

Using the distance formula: $$\sqrt{(5 - 2)^2 + (y - 9)^2} = \sqrt{34}$$ . Solving gives y = 14.

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

Using the midpoint formula: $$M = \\left(\\frac{2 + 4}{2}, \\frac{3 + 7}{2}\\right) = (3, 5)$$ .

Calculate the distance between the points (3, 4) and (3, 8).

Using the distance formula: $$d = \\sqrt{(3 - 3)^2 + (8 - 4)^2} = \\sqrt{0 + 16} = 4$$ .

What is the distance between the points (0, 0) and (5, 12)?

Using the distance formula: $$d = \\sqrt{(5 - 0)^2 + (12 - 0)^2} = \\sqrt{25 + 144} = \\sqrt{169} = 13$$ .

If the midpoint of a segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?

Using the midpoint formula: Let the other endpoint be (x, y). Then: $$4 = \\frac{2 + x}{2} \\Rightarrow x = 6$$ and $$5 = \\frac{3 + y}{2} \\Rightarrow y = 7$$ . The other endpoint is (6, 7).

What is the distance between the points (-1, -1) and (2, 3)?

Using the distance formula: $$d = \\sqrt{(2 - (-1))^2 + (3 - (-1))^2} = \\sqrt{(3)^2 + (4)^2} = \\sqrt{9 + 16} = \\sqrt{25} = 5$$ .

How do you determine if two points are the same using the distance formula?

If the distance between two points (x1, y1) and (x2, y2) is 0, then the points are the same: $$d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = 0$$ .

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

Using the distance formula: $$d = \\sqrt{(1 - 1)^2 + (1 - 1)^2} = \\sqrt{0 + 0} = 0$$ .

If the distance between two points is 10, what can you say about the coordinates of those points?

The coordinates of the points must satisfy the distance formula such that $$d = 10$$ , meaning the points are 10 units apart in the coordinate plane.

Resource Library

Math

Geometry

Distance And Midpoint

Distance And Midpoint Formulas

Distance and Midpoint Formulas

Flashcard

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Mathematics

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8th - 9th Grade

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Practice Problem

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Hard

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FLASHCARD QUESTION

Front

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

Back

FLASHCARD QUESTION

Front

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

Back

FLASHCARD QUESTION

Front

Find the distance between the points (1, 2) and (4, 6).

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

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

Back

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.

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