Answer:
1). Slope = (-2)
2). Midpoint = (2, -2)
3). Slope of the perpendicular bisector = (1/2)
4). Equation of perpendicular bisector will be x - 2y = 6
Step-by-step explanation:
A line segment has the endpoints at (4, -6) and (0, 2).
1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)
2). Mid point of the line segment is given by \((\frac{x_{1}+x_{2}}{2}) , (\frac{y_{1}+y_{2}}{2})\)
Therefore midpoints of the line segment will be \(\frac{4+0}{2},\frac{-6+2}{2}\) = (2, -2)
3). Slope of the perpendicular bisector is represented by \(m_{1}.m_{2}=(-1)\)
⇒ (-2)×m2 = (-1)
⇒ \(m_{2}=\frac{1}{2}\)
4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).
Since standard equation of the line will be given as y = mx + c
\(y=\frac{1}{2}x+c\) passes through (2, -2).
\((-2) = \frac{1}{2}(2) + c\)
c = (-1) - 2 = -3
Finally the equation of perpendicular bisector will be
\(y=\frac{1}{2}x+(-3)\)
⇒ 2y = x - 6
⇒ 2y - x = -6
⇒ x - 2y = 6
