Final answer:
The question pertains to vector operations in mathematics, focusing on translations and geometric constructions to determine new positions of points and vectors. Methods like the parallelogram rule, congruent triangles, and simple proportions are likely involved.
Step-by-step explanation:
The subject of the question seems to be related to vector operations in mathematics, specifically in the context of translation and geometry. The student is likely dealing with vector addition, subtraction, and determining coordinates after certain transformations have been applied. In the cases described, these transformations include translations based on vector equations and geometric constructions.
For example, one of the tasks involves translating a shape AEFG by following a similar translation as given in a prior example with triangles. This would require applying the translation vector to the coordinates of each point in the shape.
Another scenario asks for determining the positions of houses relative to a certain reference point, which would be an application of vector translation in a real-world scenario.
In the problem involving the Moon and measuring angles, the question mentions the congruency of triangles and the use of simple proportions, indicating a need for application of geometric principles to find distances.
When dealing with resultant and difference vectors, the student would have to utilize the parallelogram rule and trigonometry to find the lengths and directions of those vectors accurately.