Questions: Find the distance between the points (8,-2) and (7,-1). 4 unit(s) sqrt(7) unit(s) 1 unit(s) sqrt(2) unit(s)

Solution Steps

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a 2D plane, we use the distance formula: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). This formula is derived from the Pythagorean theorem.

We are given two points in the Cartesian plane: \[ (x_1, y_1) = (8, -2) \quad \text{and} \quad (x_2, y_2) = (7, -1). \]

To find the distance \(d\) between the two points, we use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. \]

First, we calculate the differences: \[ x_2 - x_1 = 7 - 8 = -1, \] \[ y_2 - y_1 = -1 - (-2) = 1. \]

Now we substitute these differences into the distance formula: \[ d = \sqrt{(-1)^2 + (1)^2} = \sqrt{1 + 1} = \sqrt{2}. \]

Final Answer