Main Answer:
The translation of AABC using the vector (-2, -5) is A'(-4, -9)B'(-2, -6)C'(-1, -5), indicating a horizontal shift of -2 units and a vertical shift of -5 units for each point.
Step-by-step explanation:
The vector (-2, -5) represents a translation in the coordinate plane, with the first component (-2) indicating a horizontal shift and the second component (-5) indicating a vertical shift. Applying this vector to each point in triangle AABC results in the transformed coordinates A'(-4, -9), B'(-2, -6), and C'(-1, -5).
For point A, the horizontal shift is -2 units, moving left, and the vertical shift is -5 units, moving downward, resulting in A'(-4, -9). Similarly, point B undergoes a horizontal shift of -2 units and a vertical shift of -5 units, resulting in B'(-2, -6). Point C experiences a horizontal shift of -1 unit and a vertical shift of -5 units, leading to C'(-1, -5).
This transformation is a basic operation in linear algebra, providing a practical understanding of how vectors can be used to alter the positions of geometric shapes in a coordinate system.