Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points in simplest radical form. (8,6) and (5,2) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Find the horizontal and vertical distances

The horizontal distance \( \Delta x\) between \(x\)-coordinates: \(|8 - 5|=3\).
The vertical distance \( \Delta y\) between \(y\)-coordinates: \(|6 - 2| = 4\).

Step2: Apply the Pythagorean theorem

Let \(d\) be the distance between the two points. By the Pythagorean theorem \(d=\sqrt{(\Delta x)^{2}+(\Delta y)^{2}}\).
Substitute \(\Delta x = 3\) and \(\Delta y=4\) into the formula: \(d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\).

Answer:

The distance between the points \((8,6)\) and \((5,2)\) is \(5\).