Answer:
[tex]\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17[/tex]
Step-by-step explanation:
Given the points
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\mathrm{The\:distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)\mathrm{\:is\:}[/tex]
[tex]=\sqrt{\left(9-1\right)^2+\left(15-0\right)^2}[/tex]
[tex]=\sqrt{8^2+\left(15-0\right)^2}[/tex]
[tex]=\sqrt{8^2+15^2}[/tex]
[tex]=\sqrt{64+225}[/tex]
[tex]=\sqrt{289}[/tex]
[tex]=\sqrt{17^2}[/tex]
[tex]=17[/tex] ∵ [tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]
Therefore,
[tex]\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17[/tex]
