Example 2

Find the distance between the points \(A(-4, -3)\) and \(B(5, 7)\).

Solution

\begin{align}\text{In this case},\ x_1 &= -4, x_2 = 5, y_1 = -3\ \text{and}\ y_2 = 7.\\\\ AB^2 &= (x_2\ –\ x_1)^2 + (y_2\ –\ y_1)^2\\\\ &= (5 - (-4))^2 + (7 - (-3))^2\\\\ &= 9^2 + 10^2\\\\ &= 181\\\\ \text{Thus}, AB &= \sqrt{181}\end{align}

Note that we could have chosen \(x_1 = 5, x_2 = -4, y_1 = 7\ \text{and}\ y_2 = -3\) and obtained the same result. As long as \((x_1, y_1)\) refers to one point and \((x_2, y_2)\) to the other point, it does not matter which one is which.