Final answer:
25% of the total area of the rectangle lies in Quadrant III. This is calculated by dividing the area of the rectangle in Quadrant III, which is one-fourth of the total area or 6.25 square units, by the total area of 25 square units and then multiplying by 100.
So, the correct answer is D.
Step-by-step explanation:
To find out what percent of the total area of the rectangle lies in Quadrant III, we must first locate the rectangle on the coordinate plane.
The rectangle's vertices are (-1, -2), (4, -2), (4, 3), and (-1, 3). By plotting these points, we see that the rectangle is positioned across quadrants II, III, and IV, with two of its sides lying on the axes.
The total width of the rectangle is the distance between the x-coordinates of the left and right vertices, which is 4 - (-1) = 5 units. The total height is the distance between the y-coordinates of the bottom and top vertices, which is 3 - (-2) = 5 units. Therefore, the total area of the rectangle is width × height = 5 units × 5 units = 25 square units.
Quadrant III is the bottom left quarter of the coordinate plane, so the area of the rectangle that lies in this quadrant is one-fourth of the total area. This means that the area in Quadrant III is 25 square units / 4 = 6.25 square units.
To find the percent of the area that lies in Quadrant III, we calculate (Quadrant III area / total area) × 100 = (6.25 / 25) × 100 = 25%.
Therefore, the answer is d. 25% of the total area of the rectangle lies in Quadrant III.