Introduction to Three Dimensional Geometry · Class 11 · CBSE · Science Mathematics
A point P lies in the xz-plane, is 5 units from the xy-plane, and is 3 units from the yz-plane. Find all possible coordinates of P.
Practice question from Introduction to Three Dimensional Geometry (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · Subjective · Q-AAD833
A point P lies in the xz-plane, is 5 units from the xy-plane, and is 3 units from the yz-plane. Find all possible coordinates of P.
Answer: Since P lies in the xz-plane, its y-coordinate is 0. Its distances from the xy-plane and yz-plane are |z| and |x| respectively, so |z| = 5 and |x| = 3. Therefore, the possible coordinates are (3, 0, 5), (3, 0, -5), (-3, 0, 5), and (-3, 0, -5).
Solution
A point in the -plane has . The distance from the -plane is , and the distance from the -plane is , giving and .
More from Introduction to Three Dimensional Geometry
- The perpendicular distance of the point P(-3, 5, -7) from the xy-plane is:
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