Final answer:
To translate a point 3 units left and 5 units down, subtract 3 from the x-coordinate and 5 from the y-coordinate. Option b is correct if the original coordinates were (1, 3), resulting in (-2, -2) after the translation.
Step-by-step explanation:
If quadrilateral ABCD is translated 3 units to the left and 5 units down, the coordinates of point B after the translation can be found by subtracting 3 from the x-coordinate and 5 from the y-coordinate of point B's original position. Let's assume that the original coordinates of point B are (x, y). After the translation, the new coordinates will be (x - 3, y - 5).
Without the original coordinates of point B, we can't determine the exact new coordinates, but we can answer the conceptual aspect of the question. The original point is translated leftward and downward in the coordinate system, corresponding to a negative direction on the x-axis and a negative direction on the y-axis, respectively.
The correct option will be the one that follows this rule. Let's analyze the given options:
Option b is the only one that represents a point that has been translated 3 units to the left and 5 units down. Therefore, if the original coordinates of point B were (1, 3), the new coordinates after translation would be (-2, -2), making option b the correct answer.