Question

current objective use the distance formula, given two points question find the distance between the points (6, -3) and (4, 3). give an exact answer in simplest radical form. do not round.

Explanation:

Step1: Recall the 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 the coordinates

Here, \(x_1 = 6\), \(y_1 = -3\), \(x_2 = 4\), \(y_2 = 3\).

Step3: Substitute into the formula

First, calculate the differences: \(x_2 - x_1 = 4 - 6 = -2\) and \(y_2 - y_1 = 3 - (-3) = 6\).
Then, square these differences: \((-2)^2 = 4\) and \(6^2 = 36\).
Add the squared differences: \(4 + 36 = 40\).
Finally, take the square root: \(d = \sqrt{40}\). Simplify \(\sqrt{40}\) as \(\sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\).

Answer:

\(2\sqrt{10}\)