Final answer:
The locus of the point is represented by the equation x + y - z = 0.
the correct answer is option B: x + y - z = 0.
Step-by-step explanation:
In order to find the locus of a point, we need to determine the equation that represents the path of the point. Let's assume the point has coordinates (x, y, z). The sum of its distance from the xy-plane and yz-plane can be calculated as |z| + |x|. And its distance from the zx-plane is |y|. Therefore, the equation that represents the locus of the point is |z| + |x| = |y|.
Now, let's simplify this equation. We know that |a| = a if a is positive and |a| = -a if a is negative. Therefore, if we consider both cases for x, y, and z, we can simplify the equation as follows:
Case 1: x, y, and z are positive: z + x = y
Case 2: x is negative, y and z are positive: z - x = y
Case 3: y and z are negative, x is positive: -z + x = -y
Case 4: x, y, and z are negative: -z - x = -y
Combining all cases, we have four possible equations: x + y - z = 0, -x + y - z = 0, -x + y + z = 0, -x - y - z = 0. Therefore, the correct answer is option B: x + y - z = 0.