SAT Question 740bf79f: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. First, $\overline{MP}$ is the hypotenuse of right triangle $MNP$, whose legs have lengths $3$ and $4$. Therefore, $(MP{)}^2=3^2+4^2$, so $(MP{)}^2=25$ and $MP=5$. Second, because $\angle MNP$ corresponds to $\angle NQP$ and because $\angle MPN$ corresponds to $\angle NPQ$, triangle $MNP$ is similar to triangle $NQP$. The ratio of corresponding sides of similar triangles is constant, so $\frac{NQ}{MN}=\frac{NP}{MP}$. Since $MP=5$ and it's given that $MN=3$ and $NP=4$, $\frac{NQ}{3}=\frac{4}{5}$. Solving for $NQ$ results in $NQ=\frac{12}{5}$, or $2.4$.