To find the equation of the central street PQ, we need to determine the slope of the given lane passing through points A and B.
The equation -7x + 3y = -21.5 can be rewritten in slope-intercept form (y = mx + b) by solving for y:
3y = 7x - 21.5
y = (7/3)x - 7.17
The slope of the given lane is 7/3.
For the central street PQ to be perpendicular to the given lane, its slope must be the negative reciprocal of 7/3, which is -3/7.
Therefore, the equation of the central street PQ can be written in the point-slope form using point P (let's assume it has coordinates (x1, y1)):
y - y1 = -3/7(x - x1)
Since the equation does not provide the coordinates of point P, we cannot determine the exact equation of the central street PQ.
However, we can eliminate the answer choices that do not have a slope of -3/7. Checking the slopes of the given answer choices:
A. -3x + 4y = 3 -> slope = 3/4 (not -3/7)
B. 3x + 7y = 63 -> slope = -3/7 (matches the slope we need)
C. 2x + y = 20 -> slope = -2 (not -3/7)
D. 7x + 3y = 70 -> slope = -7/3 (not -3/7)
Based on this analysis, the equation that matches the slope we need (-3/7) is answer choice B: 3x + 7y = 63.