Question

find the distance between (7,9) and (1,1).

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here, \((x_1, y_1) = (1, 1)\) and \((x_2, y_2) = (7, 9)\).

Step3: Substitute into formula

Calculate \(x_2 - x_1 = 7 - 1 = 6\) and \(y_2 - y_1 = 9 - 1 = 8\). Then \(d = \sqrt{6^2 + 8^2}\).

Step4: Simplify the expression

\(6^2 = 36\), \(8^2 = 64\), so \(36 + 64 = 100\). Then \(d = \sqrt{100} = 10\).

Answer:

10