Choose the equation(s) of the perpendicular bisector of the segment with the end points A(-7, 5) and K (1, -1).Question 6Select one or more:a.y - 2 = −43−43(x - 3)b.4x - 3y = 18c.-4x + 3y = 18d.y - 2 = 4343(x + 3)

To find the equation of the perpendicular bisector of the segment with the end points A(-7, 5) and K (1, -1), we need to follow these steps:

1. Find the midpoint of the segment AK. The midpoint M is given by the formula M = [(x1 + x2)/2 , (y1 + y2)/2]. So, M = [(-7 + 1)/2 , (5 - 1)/2] = [-3, 2].

2. Find the slope of the line AK. The slope is given by the formula (y2 - y1) / (x2 - x1). So, the slope of AK = (-1 - 5) / (1 - (-7)) = -6/8 = -3/4.

3. The slope of the line perpendicular to AK is the negative reciprocal of the slope of AK. So, the slope of the perpendicular bisector = -1/(-3/4) = 4/3.

4. Use the point-slope form of the equation of a line to find the equation of the perpendicular bisector. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. So, the equation of the perpendicular bisector is y - 2 = 4/3(x - (-3)).

5. Simplify the equation to get it in the form y = mx + b. So, y - 2 = 4/3x + 4, which simplifies to y = 4/3x + 6.

Comparing this with the given options, none of them match the equation we found. So, none of the options a, b, c, or d is the equation of the perpendicular bisector of the segment with the end points A(-7, 5) and K (1, -1).