MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

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

[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