Question

Distance between (1,-2) and (4,4)

Answer 1

$\bf\textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ -2}})\quad % (c,d) &({{ 4}}\quad ,&{{ 4}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[4-1]^2+[4-(-2)]^2}\implies d=\sqrt{(4-1)^2+(4+2)^2} \\\\\\ d=\sqrt{3^2+6^2}\implies d=\sqrt{45}\implies d=\sqrt{3\cdot 3\cdot 5}\implies d=\sqrt{3^2\cdot 5} \\\\\\ d=3\sqrt{5}$