Final answer:
The correct answer for the slopes of a rectangular patio represented on a coordinate grid, with one side having a slope of 'G', is (a) G, 0. This indicates there will be one slope G for the opposite side and two slopes of 0 for the adjacent sides, indicating parallel and perpendicular relationships between sides of a rectangle.
Step-by-step explanation:
The question posed is related to the geometry of rectangles and the algebra of straight lines. When designing a rectangular patio with one side represented by the line equation y = Gr + B, the opposite side of the rectangle will have the same slope (G) due to parallelism. The adjacent sides, being perpendicular to the first side, will have slopes that are negative reciprocals to the slope of the first side.
Given the options provided:
a) G, 0 - implies one side is parallel (slope G) and the adjacent sides are horizontal (slope 0), which is correct for a rectangle.
b) 1, 2
c) 3, 4
d) 5, 6
Option (a) is correct because a horizontal line (slope of 0) is perpendicular to any vertical line (undefined slope), adhering to the right angle criterion of the rectangle.
From Figure A1, we can deduce that the value of the slope determines the direction of the incline of a line on a graph. A slope of 'G' would represent the 'rise over run' or the steepness of a side, and a slope of '0' signifies a horizontal line, which in the context of rectangle sides, means the side is parallel to the x-axis.