Question

The given line segment has a midpoint at (3, 1).

Answer 1

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 2

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 = $\frac{4-(-2)}{2-4}$

=$\frac{6}{-2}$

= -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 =$\frac{1}{3}$

Now equation of perpendicular bisector of AB passing through C(3,1)  is

$y -1 =\frac{1}{3}(x-3)$

$y= 1+\frac{1}{3}x -1$

$y=\frac{1}{3}x$

Hence the equation of line is y =x/3