Tony took the city bus from the local library located at (4, 0) on a coordinate plan map to his dorm located at (12, 6) on the map. If each unit represents 0.75 miles, how far is his dorm from the library?

well, first off, let's check how far is it on the map, from the library to his dorm,

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 4}}\quad ,&{{ 0}})\quad % (c,d) &({{ 12}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{(12-4)^2+(6-0)^2}\implies d=\sqrt{8^2+6^2}\implies d=\sqrt{64+36} \\\\\\ d=\sqrt{100}\implies d=10[/tex]

so there are that many units, now, how many miles is that?

well, we know each map unit is 0.75 miles, so there are d * 0.75 miles then