Question

The coordinates of the endpoints of line segment C D are C(3, 8) and D(6, -1). Express the length of line segment C D in simplest radical form.

Answer 1

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) C&({{ 3}}\quad ,&{{ 8}})\quad % (c,d) D&({{ 6}}\quad ,&{{ -1}}) \end{array}\qquad d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ CD=\sqrt{(6-3)^2+(-1-8)^2}\implies CD=\sqrt{3^2+(-9)^2} \\\\\\ CD=\sqrt{9+81}\implies CD=\sqrt{90}\quad \begin{cases} 90=2\cdot 3\cdot 3\cdot 5\\ \qquad 2\cdot 3^2\cdot 5\\ \qquad 10\cdot 3^2 \end{cases} \\\\\\ CD=\sqrt{10\cdot 3^2}\implies CD=3\sqrt{10}$