here's an animation that illustrates how they miss each other. The green line is the "line of nodes" and represents where the orbital planes of the orbits cross. The small spheres on the orbits show the relative positions of Neptune and Pluto when their orbits "cross"(when they exchange positions as to order in distance from the sun.)
The small circle in the center is the Earth's orbit. So even though there is a point where the orbits look like they pass fairly near each other, when compared to the size of Earth's orbit we can see that even at their closest, they miss by quite a large distance.
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