SAT Question 6a3fbec3: Lines, Angles, and Triangles answer and explanation with Desmos solution

According to the properties of right triangles, $BD$ divides triangle $ABC$ into two similar triangles, $ABD$ and $BCD$. The corresponding sides of $ABD$ and $BCD$ are proportional, so the ratio of $BD$ to $AD$ is the same as the ratio of $DC$ to $BD$. Expressing this information as a proportion gives $\frac{6}{8}=\frac{DC}{6}$. Solving the proportion for $DC$ results in $DC=4.5$. Note that 9/2, 4.5, and 4.50 are examples of ways to enter a correct answer.