Questions covered in Basic

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. A point is on the x-axis. What are its y-coordinate and z-coordinate?
2. The point $(-3, 1, -2)$ lies in which octant?
3. The distance of the point $(3, 4, 5)$ from the origin is
4. The coordinates of the midpoint of the line segment joining $(2, 3, 4)$ and $(4, 1, -2)$ are
5. If the distance between the points $(a, 0, 1)$ and $(0, 1, 2)$ is $\sqrt{27}$, then the value of $a$ is
6. Find the distance between the points $P(-1, 3, -4)$ and $Q(1, -3, 4)$.
7. Show that the points $P(-2, 3, 5)$, $Q(1, 2, 3)$ and $R(7, 0, -1)$ are collinear.
8. Find the coordinates of the point which divides the line segment joining the points $(1, -2, 3)$ and $(3, 4, -5)$ in the ratio $2:3$ internally.
9. Find the ratio in which the YZ-plane divides the line segment formed by joining the points $(-2, 4, 7)$ and $(3, -5, 8)$.
10. Find the coordinates of the centroid of the triangle with vertices $(3, -5, 7)$, $(-1, 7, -6)$ and $(1, 1, 2)$.
11. Find the coordinates of the fourth vertex of the parallelogram whose three vertices are $A(1, 2, 3)$, $B(3, 4, 5)$ and $C(-1, 0, 2)$.
12. Case Study: A point $P$ has coordinates $(2, 3, 4)$.
    (i) Find the distance of P from the x-axis.
    (ii) Find the coordinates of the foot of the perpendicular from P on the XY-plane.
    (iii) Find the image of P in the XZ-plane.