Distance Formula

The Distance Formula is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ , which calculates the distance between two points (x1, y1) and (x2, y2) in a Cartesian plane.

Using the Distance Formula: $$d = \sqrt{(8 - (-3))^2 + (-42 - (-11))^2} = \sqrt{(11)^2 + (-31)^2} = \sqrt{121 + 961} = \sqrt{1082} \approx 32.9$$ .

The correct expression is: $$d = \sqrt{(9 - 1)^2 + (5 - 2)^2}$$ .

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

Using the Distance Formula: $$d = \sqrt{(1 - 4)^2 + (1 - 7)^2} = \sqrt{(-3)^2 + (-6)^2} = \sqrt{9 + 36} = \sqrt{45} \approx 6.71$$ .

Using the Distance Formula: $$d = \sqrt{(1 - 2)^2 + (5 - 9)^2} = \sqrt{(-1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.12$$ .

The 'x-coordinate' refers to the horizontal position of a point in a Cartesian plane, indicating how far left or right the point is from the origin.

The 'y-coordinate' refers to the vertical position of a point in a Cartesian plane, indicating how far up or down the point is from the origin.

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

The first step is to identify the coordinates of the two points you are measuring the distance between.