In the diagram, what is the length of $B D$ ?
(A) 13
(B) 17
(C) $\sqrt{205}$
(D) $\sqrt{160}$
(E) 15

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-033.jpg?height=366&width=393&top_left_y=213&top_left_x=1300)

Part C: Each correct answer is worth 8.
Points $D$ and $C$ have equal $y$-coordinates, -3 , and so side $D C$ is parallel to the $x$-axis and has length $3-(-2)=5$.

Points $B$ and $C$ have equal $x$-coordinates, 3 , and so side $B C$ is parallel to the $y$-axis and has length $9-(-3)=12$.

That is, in $\triangle B C D$, sides $D C$ and $B C$ are perpendicular or $\angle B C D=90^{\circ}$ with $B C=9$ and $D C=5$.

Using the Pythagorean Theorem, $B D^{2}=D C^{2}+B C^{2}=5^{2}+12^{2}$ and so $B D^{2}=25+144=169$ or $B D=\sqrt{169}=13($ since $B D>0)$.