Distance on the Coordinate Plane

Front

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

Back

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Front

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

Back

The distance is \(d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\).

Front

What does the distance formula represent in geometry?

Back

The distance formula calculates the straight-line distance between two points in a two-dimensional space.

Front

Find the distance between the points (–6, –10) and (–2, –10).

Back

The distance is \(d = \sqrt{(-2 - (-6))^2 + (-10 - (-10))^2} = \sqrt{4^2 + 0^2} = 4\).

Front

What is the significance of the square root in the distance formula?

Back

The square root ensures that the distance is a non-negative value, as distance cannot be negative.

Front

If the points are (3, 4) and (3, 8), what is the distance?

Back

The distance is \(d = \sqrt{(3 - 3)^2 + (8 - 4)^2} = \sqrt{0 + 16} = 4\).

Front

How do you find the distance between two points on a horizontal line?

Back

If two points have the same y-coordinate, the distance is the absolute difference of their x-coordinates.

Front

How do you find the distance between two points on a vertical line?

Back

If two points have the same x-coordinate, the distance is the absolute difference of their y-coordinates.

Front

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

Back

The distance is \(d = \sqrt{(4 - 1)^2 + (5 - 1)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\).

Front

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

Back

The distance is \(d = \sqrt{(5 - 0)^2 + (12 - 0)^2} = \sqrt{25 + 144} = \sqrt{169} = 13\).