Posted by Will on .
what is the equation for the perpendicular bisector of the line segment whose endpoints are (-7,2) (-1,-6)
bisector is the line that cuts the segment into half and is perpendicular to it. So first we need to find the midpoint M of segment ; x coordinate of M; (-7+-1)/2=-8/2=-4. y coordinate of M; (2+-6)/2= -4/2=-2.So M(-4,-2)
As lines are perpendicular their gradients will be opposite & reciprocal. Lets find the gradient of AB: (2--6)/(-7--1)= 8/-6=-4/3. So gradient of line; 3/4
Equation of line; y=mx+c so substituting coordinates x,y and gradient m we get; -2=3/4(-4)+c solving for c we get; c=1 so line is; y=(3/4)x+1
Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).