Final answer:
The perpendicular bisector of the segment with endpoints (-2, -2) and (-1, 2) is not correctly represented by any of the given answer choices. The correct slope for the bisector should be -1/4, but the corresponding 'b' value appears to be incorrect in the options provided.
Step-by-step explanation:
To find the equation of the perpendicular bisector of the segment with endpoints (-2, -2) and (-1, 2), follow these steps: Calculate the midpoint of the segment, which will be a point on the bisector. Find the slope of the segment, then find the negative reciprocal to get the slope of the bisector. Use the slope of the bisector and the midpoint to write the equation in y=mx+b form. The midpoint is ((-2 - 1)/2, (-2 + 2)/2) = (-3/2, 0). The slope of the segment is (2 - (-2))/(-1 - (-2)) = 4. The perpendicular slope is the negative reciprocal, which is -1/4. Using the point-slope form y - y1 = m(x - x1), we plug in the midpoint and the slope of the bisector: y - 0 = -1/4(x - (-3/2)), which simplifies to y = -1/4x - 3/8. This choice is not among the provided options, indicating a potential error in the question or answer choices. If we assume an error and check the provided answers for perpendicularity with the original line's slope of 4, we find y = -1/4x -2 has the correct perpendicular slope. However, the value of b is incorrect if we base it on the calculated midpoint (-3/2, 0), since -1/4*(-3/2) + b should equal 0, and b should be 3/8 when corrected for the error.