Question

calculate the distance between the points l = (-7, 2) and e = (-3, 6) in the coordinate plane. give an exact answer (not a decimal approximation).

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

For \(L = (-7, 2)\), \(x_1 = -7\), \(y_1 = 2\); for \(E = (-3, 6)\), \(x_2 = -3\), \(y_2 = 6\).

Step3: Substitute into formula

Calculate \(x_2 - x_1 = -3 - (-7) = 4\), \(y_2 - y_1 = 6 - 2 = 4\). Then \(d = \sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32}\).

Step4: Simplify the radical

\(\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}\).

Answer:

\(4\sqrt{2}\)