Introduction to Three Dimensional Geometry quiz

The number of octants in space is:

The point (0, 0, 5) lies on the:

The equation of the XY-plane is:

The distance of (3, 4, 0) from the origin is:

The point (-2, -3, -4) lies in the octant:

The coordinates of a point in the YZ-plane have the form:

The distance between (1, 1, 1) and (2, 2, 2) is:

The perpendicular distance of (3, -4, 5) from the XY-plane is:

The foot of the perpendicular from (2, 3, 4) to the x-axis is:

The points (1, 2, 3), (2, 3, 4) and (3, 4, 5) are:

Name the octants in which (1, -2, 3) and (-4, 2, -5) lie. (2 marks)

Find the distance between (-3, 7, 2) and (2, 4, -1). (2 marks)

Find the distance between (-1, 3, -4) and (1, -3, 4). (2 marks)

What are the coordinates of the foot of the perpendicular from (3, -1, 4) to the XY-plane? (2 marks)

Show that (0, 0, 0), (2, 0, 0) and (1, sqrt3, 0) form an equilateral triangle. (2 marks)

Find the perimeter of the triangle with vertices (0, 4, 0), (6, 0, 0) and (0, 0, 0). (2 marks)

If the distance between (3, 2, k) and (1, 2, 3) is 2sqrt2, find k. (2 marks)

What are the signs of the coordinates of a point in the octant X'OYZ'? (2 marks)

Find the coordinates of the point on the z-axis equidistant from (1, 5, 7) and (5, 1, -4). (2 marks)

Find the distance of the point (4, -3, 12) from the origin. (2 marks)

Find the lengths of the sides of the triangle with vertices A(3, -1, 2), B(5, 2, 4) and C(1, 4, 2), and find its perimeter. (3 marks)

Find k if the distance between (5, -1, 7) and (k, 5, 1) is 9 units. (3 marks)

Find the coordinates of the point on the y-axis equidistant from (3, 1, 2) and (5, 5, 2). (3 marks)

A cube has one vertex at the origin and three edges of length 4 along the positive axes. Find the length of its diagonal from the origin. (3 marks)

Show that the points (1, 2, 3), (-1, -2, -1), (2, 3, 2) and (4, 7, 6) have opposite sides of equal length. (3 marks)

Read the passage and answer the questions. A drone takes off from a point O on the ground, which is taken as the origin. It flies to a point A that is 30 m east, 40 m north and 50 m high. Take east as the x-axis, north as the y-axis and up as the z-axis. (i) Write the coordinates of A. (ii) Find the distance OA. (iii) Find the distance of A from the ground. (5 marks)

Read the passage and answer the questions. A room is 6 m long, 4 m wide and 3 m high. One corner of the floor is taken as the origin, and the edges along the floor and wall are the axes. A lamp hangs from the centre of the ceiling. (i) Write the coordinates of the lamp. (ii) Find the distance of the lamp from the origin. (iii) Find the coordinates of the corner of the ceiling opposite the origin. (5 marks)

Read the passage and answer the questions. Two satellites are at points P(2, 3, 6) and Q(-2, 3, 3), with distances in thousands of kilometres from the centre of the Earth taken as the origin. (i) Find the distance of P from the origin. (ii) Find the distance PQ. (iii) Which satellite is closer to the Earth's centre? (5 marks)

Read the passage and answer the questions. A point moves in space so that it is always at a distance of 5 units from the origin. (i) Write the equation of its path. (ii) What is this surface called? (iii) Does the point (3, 4, 0) lie on it? (5 marks)

Read the passage and answer the questions. The points A(2, 1, 3), B(5, 2, 1) and C(8, 3, -1) are given. (i) Find AB. (ii) Find BC and AC. (iii) Are the points collinear? Explain. (5 marks)

Explain the three-dimensional coordinate system, coordinate axes, coordinate planes and octants with a figure. Give the signs of coordinates in each octant. (6 marks)

Derive the distance formula between two points in space. (6 marks)

Show that the points A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6) form a right-angled isosceles triangle. (6 marks)

Find the equation of the set of points P whose distances from A(3, 4, -5) and B(-2, 1, 4) are equal. (6 marks)

Find the coordinates of a point equidistant from the four points O(0, 0, 0), A(2, 0, 0), B(0, 3, 0) and C(0, 0, 8). (6 marks)