Final Answer:
The slope of segment SR is b) -12.
Step-by-step explanation:
In a trapezoid, opposite sides are parallel. If segment PQ has a slope of 12, then the opposite side SR must have a negative reciprocal slope to maintain parallelism. The negative reciprocal of 12 is -1/12. Therefore, the correct answer is b) -12.
To understand this, let's delve into the mathematical explanation. The slope of a line (m) is given by the change in y divided by the change in x (m = Δy/Δx). In this context, the slope of segment PQ is 12, which means for every 1 unit increase in x, there is a 12-unit increase in y. To find the slope of the parallel side SR, we need the negative reciprocal. The negative reciprocal of 12 is -1/12, implying that for every 1 unit increase in x along SR, there is a 1/12 unit decrease in y. This maintains the parallel relationship between PQ and SR.
In summary, understanding the concept of slopes in parallel lines is crucial. The negative reciprocal relationship ensures that the trapezoid's opposite sides are parallel. Therefore, the slope of segment SR is -1/12, leading to the final answer of b) -12.