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In three-dimensional coordinate systems, calculating the distance from a point to a specific plane is a fundamental concept. Understanding this helps to grasp more advanced topics like plane equations and geometrical properties.
In this context, let's focus on the yz-plane. The yz-plane consists of all points where the x-coordinate is zero. Thus, the distance of any point \((x, y, z)\) from the yz-plane is simply the absolute value of its x-coordinate, represented mathematically as \(|x|\).
This might seem a bit abstract, but it's quite straightforward. Imagine drawing a perpendicular from the point to the yz-plane. This shortest straight line corresponds to the x-coordinate's absolute value value.
For example, for point \((-4, 0, -1)\), the distance to the yz-plane is \(|-4| = 4\). Similarly, for point \((3, 1, -5)\) it is \(|3| = 3\), and for point \((2, 4, 6)\) it's \(|2| = 2\). Comparing these, point \(2, 4, 6\) has the smallest distance, meaning it is closest to the yz-plane.

The yz-plane is one of the fundamental planes in a Cartesian coordinate system. Its defining feature is that all points on this plane have their x-coordinate equal to zero.
This plane essentially represents a two-dimensional surface where the x-axis does not influence positioning, focusing solely on the y and z coordinates.
In simpler terms, it's like a vertical wall extending infinitely in the y and z directions, with no movement in the x direction.
Understanding the yz-plane's properties assists in visualizing spatial relations and ensures clarity in problems involving distances and intersections. In exercises, when tasked to identify proximity to the yz-plane, one needs to check the smallest absolute value of x among given points. This absolute value determines how 'far' the point is from residing directly on the plane.

The xz-plane shares similarities with the yz-plane but differs crucially by having zero y-coordinates for points that rest on it. Conceptually, this plane resembles a flat surface extending indefinitely in both x and z directions, lying horizontally.
This is as if you're looking at a field that stretches away from you in width and depth but has no height—the height being the y-axis in this analogy.
To determine if a point lies on the xz-plane, check if its y-coordinate equals zero. In the given exercise, point \((-4, 0, -1)\) lies on this plane because its y-coordinate is zero.
The practical knowledge of the xz-plane's characteristics helps solve problems involving locating points, lines, and intersections within the three-dimensional space.