A: $(3,-4,5)$ B: $(0,-4,0)$ C: $(0,-4,5)$
Work Step by Step
Given the two vertices, we find the peak value for each coordinate is $x=3$, $y=-4$, and $z=5$. A is directly on top of the vertex $(3,-4,0)$, meaning that only the $z$ coordinate is different. C is on the same plane as $(0,0,5)$, making the $z$ coordinate $10$. Thus, A is at $(3,-4,5)$. B is on the $yz$-plane and $xy$-plane, so the $x$ and $z$ coordinate is zero. Thus, B is at $(0,-4,0)$. C is on the $yz$-plane, so the $x$ coordinate is zero. Thus, C is at $(0,-4,5)$.