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

Step-by-step explanation:

I think the attached photo supports for your question

Here is my anser:

We need to find the slope of the of and 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 : = -3

But 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.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

a

step-by-step explanation: