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 side - lengths

The two points are $(x_1,y_1)=(8,6)$ and $(x_2,y_2)=(5,2)$. The horizontal side - length (difference in x - coordinates) $a=\vert x_1 - x_2\vert=\vert8 - 5\vert = 3$. The vertical side - length (difference in y - coordinates) $b=\vert y_1 - y_2\vert=\vert6 - 2\vert = 4$.

Step2: Apply the Pythagorean theorem

The distance $d$ between the two points (the length of the hypotenuse of the right - triangle) is given by the Pythagorean theorem $d=\sqrt{a^{2}+b^{2}}$. Substitute $a = 3$ and $b = 4$ into the formula: $d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

$5$