ethancappell123
Answered

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



What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

y = x

y = x – 2
y = 3x
y = 3x − 8

The given line segment has a midpoint at (3, 1). What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment? y = x y class=

Answer :

altavistard
Wow.  Nice that you've shared this great graph!!

We need to find the slope of the blue given line to determine the slope of the perpendicular bisector of this blue line.

From the graph, we see that if x increases from 2 to 4, y decreases from 4 to -2.  Thus, the slope of the blue line is [-2-4] divided by 4-2, or m = -6/2, or m = -3.

The slope of the perpend. bisector of the blue line is the negative reciprocal of -3, or  m= 1/3.

Let's find the slope-intercept form of this bisector.  We need to determine b in y=mx+b.  Referring to the midpoint of the blue line, x= 3; y= 1; and m=1/3.  Then

y=mx+b becomes 1=(1/3)(3) + b.   Solving for b:  1=1+b.  Then b=0.

Thus, the equation of the perpendicular bisector of the blue line through (3,1) is  y=mx + b, or y=(1/3)x + 0, or y=x/3.


akposevictor

The equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.

What is the Slope-intercept Form of an Equation?

The slope-intercept form is given as, y = mx + b.

b is y-intercept, and m is the slope.

Slope = change in y/change in x.

The slopes of two lines that are perpendicular to each other are negative reciprocal of each other.

Thus, let's find the slope of the blue line:

Slope = (-2 - 4)/(4 - 2) = -3

Therefore, the slope of the line perpendicular to it would be, 1/3.

Equation of the perpendicular bisector that passes through (3, 1):

Since slope (m) is 1/3, find b by substituting m = 1/3 and (x, y) = (3, 1) into y = mx + b.

Thus:

1 = 1/3(3) + b

1 = 1 + b

1 - 1 = b

b = 0.

Substitute b = 0, and m = 1/3 into y = mx + b:

y = 1/3x + 0

y = 1/3x

Therefore, the equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.

Learn more about slope-intercept form on:

https://brainly.com/question/25826868

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