Final answer:
To find the general form of an equation for the perpendicular bisector of a line segment, calculate the slope of the line segment, find the negative reciprocal of that slope, and use the point-slope form of a linear equation to derive the general form. The correct answer is x + 3y = 19.
Step-by-step explanation:
The general form of an equation for the perpendicular bisector of a line segment with endpoints A(6,-5) and B(0,-13) can be found by finding the slope of the line segment and then finding the negative reciprocal of that slope.
1. Find the slope of the line segment using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) = A(6,-5) and (x2, y2) = B(0,-13).
2. Take the negative reciprocal of the slope to find the slope of the perpendicular bisector.
3. Use the point-slope form of a linear equation y - y1 = m(x - x1) where (x1, y1) is one of the midpoint of the line segment and m is the slope of the perpendicular bisector. Substitute the values and simplify to get the equation in general form.
The general form of the equation for the perpendicular bisector is x + 3y = 19, so the correct answer is (c) x + 3y = 19.