The perpendicular bisector to the line segment with endpoints (-3,6) and (9,2) the equation of the line is y=

y = 3x-5

===========================================================

Explanation:

First find the slope of the line through the two given points. Use the slope formula for this. See figure 1 in the attached images. After following those steps, the slope happens to be -1/3. From here, you flip the fraction to get -3/1 and then you flip the sign to get +3/1 or just 3/1 which is equivalent to 3. This is the slope of the perpendicular line. The slope of the answer is m = 3, which we'll use later to help determine the y intercept.

Before we can find the y intercept, we need to know what point is on this perpendicular bisector. Recall that "bisect" means to "cut in half". So we need to find the point that cuts the segment from (-3,6) to (9,2) in half. In short: we need the midpoint. Refer to figure 2 (attached image below) to see how I found the midpoint. The short version is that you add up the corresponding coordinates and then divide by 2. The midpoint found is (3,4)

Using this midpoint (x,y) = (3,4), we can find the y intercept denoted b

y = mx+b

y = 3x+b .... plug in the slope m = 3

4 = 3*(3)+b ... plug in the point (x,y) = (3,4)

4 = 9 + b

4-9 = 9+b-9 .... subtract 9 from both sides

-5 = b

b = -5

So if m = 3 is the slope and b = -5 is the y intercept, then y = mx+b turns into y = 3x-5 which is the answer we want.

sadsadsadsad

step-by-step explanation: