Answer:
y = 1/3 x.
Step-by-step explanation:
The slope of the given line is
(4 - (-2) / 2 - 4)
= -3.
So the slope of the line perpendicular to it = -1 / (-3) = 1/3.
This line also passes through the point (3, 1) so its equation is ( by the point-slope form):
y - 1 = 1/3(x - 3)
y - 1 = 1/3x - 1
y = 1/3 x (answer).
Answer: The answer is y= x/3
Step-by-step explanation:
Given points =(2,4) and (4,-2) whose mid point is (3,1)
Let the points be named as A(2,4) and B(4,-2) and mid point as C(3,1)
So slope of AB = [tex]\frac{4-(-2)}{2-4}[/tex]
=[tex]\frac{6}{-2}[/tex]
= -3
We know that Product of Slope of perpendicular lines = -1
Now slope of the line perpendicular to AB × slope of AB = -1
-3 × m2 =-1
i.e. m2 =[tex]\frac{1}{3}[/tex]
Now equation of perpendicular bisector of AB passing through C(3,1) is
[tex]y -1 =\frac{1}{3}(x-3)\\[/tex]
[tex]y= 1+\frac{1}{3}x -1[/tex]
[tex]y=\frac{1}{3}x[/tex]
Hence the equation of line is y =x/3
