Question

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

Answer 1

Answer:

if I had to guess (which I'm not, i said "if". get your facts straight young boi) I'd say A

Answer 2

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.