Q5. Find the mirror images of P(1, −2, 3) in the YZ-, ZX- and XY-planes.
Each mirror changes the sign of the coordinate that is 0 on it: (−1, −2, 3), (1, 2, 3) and (1, −2, −3).
Q6. A point is on the y-axis, 4 units from the origin on the side of OY′. Write its coordinates.
(0, −4, 0).
Q7. A point is in the YZ-plane, 3 units above the XY-plane and 2 units to the left of the ZX-plane. Find it.
In the YZ-plane x = 0; to the left of the ZX-plane y = −2; above the XY-plane z = 3. The point is (0, −2, 3).
Q8. Find the feet of the perpendiculars from (−6, 2, −1) to the z-axis and to the ZX-plane.
(0, 0, −1) on the z-axis and (−6, 0, −1) on the ZX-plane.
Q9. For the box with O and P(3, −1, 2) at opposite corners, find the non-origin corner on the y-axis and the corner diagonally opposite O in the ZX-plane face.
(0, −1, 0) on the y-axis and (3, 0, 2) in the ZX-plane.
Q10. Which of (0, 0, 7), (0, 3, 0), (2, 0, −5) and (0, 4, 1) lie on an axis, and which lie on a coordinate plane but not on an axis?
(0, 0, 7) is on the z-axis and (0, 3, 0) on the y-axis. (2, 0, −5) is in the ZX-plane and (0, 4, 1) in the YZ-plane, off the axes.
Q11. The point (a − 2, b + 1, c) lies on the x-axis. Find b and c.
On the x-axis the second and third coordinates are 0: b + 1 = 0 and c = 0, so b = −1 and c = 0. Any a will do.
Q12. The mirror image of a point P in the XY-plane is (2, −1, 4). Find P, and the image of P in the YZ-plane.
Reflecting back, P = (2, −1, −4). Its image in the YZ-plane is (−2, −1, −4).