Final answer:
The gradient of the straight line SR, where S is the midpoint of PQ, is calculated to be -2/3, which is not listed in the options provided.
Step-by-step explanation:
To find the gradient of the straight line SR, we need to find the coordinates of point S, which is the midpoint of the line segment PQ, and then use these coordinates with the coordinates of point R to calculate the gradient.
Step 1: Find the coordinates of S, the midpoint of PQ. The formula for the midpoint is ((x1 + x2) / 2, (y1 + y2) / 2). So, for points P(6,8) and Q(2,2), S would be located at ((6+2)/2, (8+2)/2) = (4, 5).
Step 2: Calculate the gradient of SR. The gradient (slope) formula is ((y2 - y1) / (x2 - x1)). Using points S(4, 5) and R(-2, 9), the gradient would be (9 - 5) / (-2 - 4) = 4 / -6 which simplifies to -2/3.
Therefore, the gradient of the straight line SR is not represented by any of the provided options A. -2, B. -1, C. 1, or D. 2. There seems to be a mistake because the actual calculated gradient is -2/3.