AN EXAMPLE OF A TRANSFORMATION IN THE COORDINATE PLANE AND AN EXPLANATION ON WHETHER CONGRUENT OR SIMILAR FIGURES ARE CREATED AND WHY.

Span: Select one of the following: 1. A plane through the origin. 2. A line through the origin. 3. R3 4. Origin.

Question 2 a) An aircraft, flying in a straight line, passes through the points (-6,7,2) and (-3,2,3) measured in kilometres. Find the vector form of the equation of the line that describes the flight path of the aircraft. Determine whether or not the aircraft is flying parallel to the ground which is described by the plane -4x + 6y + 42z = 17, where x.y and z are also measured in kilometres. b) A large shade sail is to be hung tautly between the tops of 3 poles. The tops of these poles are located at point A, B, and C as shown in the Figure 1 below. For instance the point A is located at (2, -3,3) m. find the vectors AB and AC and hence the equation of the plane through these three points. 3 m 5 m 2 m 0 2 m 3 m B 3 m 3 m Figure 1: The poles in Q2(b) which the large shade sail is to be hung taughtly between. c) A tunnel is being constructed through a mountain range where the tunnel is being constructed from both ends at the same time. One end of tunnel starts at the point A (80, -287,…

Point F 4. Which of the following points lie on plane R? Select all that apply. Point C Point I Point E C H R E F D P