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Gr 10 Math Ch 7: Distance between two Points

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Gr 10 Math Ch 7: Distance between two Points

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Questions and Answers

What is the formula for calculating the distance between two points A(x₁, y₁) and B(x₂, y₂)?

$d = ext{sqrt}ig{(}(x₂ - x₁)^2 + (y₂ - y₁)^2ig{)}$ (correct)

$d = rac{(x₁ - x₂)^2 + (y₁ - y₂)^2}{1/2}$

$d = rac{(x₂ - x₁)^2 + (y₂ - y₁)^2}{(x₁ + y₁)}$

$d = rac{(x₂ - x₁) + (y₂ - y₁)}{2}$

In the distance formula, what does AC represent?

The distance along the y-axis

The horizontal difference between x-coordinates (correct)

The constant value of x-coordinate

The vertical difference between y-coordinates

How does the formula for distance between two points reflect the Pythagorean theorem?

It calculates the distance by adding the y-coordinates directly.

It treats the differences in coordinates as the two legs of a right triangle. (correct)

It uses the average of the x-coordinates instead of absolute differences.

It derives the distance as a sum of angles in a triangle formed by the points.

If point A is located at (3, 4) and point B is at (6, 8), what is the distance between the two points?

$d = ext{sqrt}(25)$ Signup and view all the answers

Which statement about the distance formula is true?

The square of a negative value is always positive. Signup and view all the answers

What can be inferred if the distance between two points A(x₁, y₁) and B(x₂, y₂) is zero?

Points A and B are identical. Signup and view all the answers

If points A and B have coordinates (x₁, y₁) and (x₂, y₂) respectively, which of the following statements correctly describes the distance formula?

It produces the same result when coordinates are swapped. Signup and view all the answers

What does the expression $(x₂ - x₁)^2$ in the distance formula represent geometrically?

The square of the horizontal distance between points A and B. Signup and view all the answers

Which transformation of the distance formula correctly calculates the distance using absolute values?

distance = $|x₁ - x₂| + |y₁ - y₂|$ Signup and view all the answers

When calculating the distance between the points (4, 2) and (1, 1), which of the following is the correct computation of the distance based on the formula?

$ ext{distance} = 2.24$ Signup and view all the answers