Answer:
Step-by-step explanation:
The equation of perpendicular bisector of A(-6, -4 ) and B(2, 0) is y = -2x - 6
Solution:
Given that we have to find the equation of perpendicular bisector of A(-6, -4 ) and B(2, 0)
A perpendicular bisector, bisects a line segment at right angles
To obtain the equation we require slope and a point on it
Find the midpoint and slope of the given points and then we can find the equation
Find the midpoint:
Given points are A(-6, -4 ) and B(2, 0)
The midpoint is given as:
Substituting the values we get,
Find the slope of given points:
Then the slope of perpendicular bisector is given as:
We know that product of slopes of given line and slope of line perpendicular to it is equal to -1
Let the slope of perpendicular bisector be
Find the equation of line with slope -2 and point (-2, -2)
The equation of line in slope intercept form is given as:
y = mx + c -------- eqn 1
Where "m" is the slope and "c" is the y - intercept
Substitute (x, y) = (-2, -2) and slope m = -2 in eqn 1
-2 = -2(-2) + c
-2 = 4 + c
c = -2 - 4
c = -6
Substitute c = -6 and m = -2 in eqn 1
y = -2x - 6
Thus the required equation of perpendicular bisector is found
