What is the perpendicular bisector equation that meets the line sgment of -1 -6 and 5 -8 on the Cartesian plane showing work?

Answer 1

To find the perpendicular bisector of the line segment connecting the points (-1, -6) and (5, -8), we first calculate the midpoint of the segment. The midpoint (M) is given by:

[ M = \left( \frac{-1 + 5}{2}, \frac{-6 + (-8)}{2} \right) = \left( 2, -7 \right). ]

Next, we find the slope of the line segment, which is

[ \text{slope} = \frac{-8 - (-6)}{5 - (-1)} = \frac{-2}{6} = -\frac{1}{3}. ]

The slope of the perpendicular bisector is the negative reciprocal, which is 3. Using the point-slope form of a line, the equation of the perpendicular bisector is:

[ y + 7 = 3(x - 2). ]

This simplifies to:

[ y = 3x - 13. ]