Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).

first find the midpoint (pointof intersection): ((4-2)/2, (1+5)/2) or 1,3/2 check that.

Next find the slope of the line that connects the points: (1+5)/(4-2)=3

so the question now, is what is the equation of a line with slope -1/3, and goes through the point 1,3/2

y=mx+b
y=-1/3 x +b
to solve for b, put in the x,y point, and now you have m, and b.

To find the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5), we need to follow these steps:

Step 1: Find the midpoint of the segment.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be calculated using the following formulas:
midpoint x-coordinate = (x1 + x2) / 2
midpoint y-coordinate = (y1 + y2) / 2

In this case, the endpoints are (4, 1) and (2, -5), so we have:
midpoint x-coordinate = (4 + 2) / 2 = 6 / 2 = 3
midpoint y-coordinate = (1 + -5) / 2 = -4 / 2 = -2

So, the midpoint of the segment is (3, -2).

Step 2: Find the slope of the given segment.
The slope of a line segment is given by the formula:
slope = (y2 - y1) / (x2 - x1)

Using the endpoints (4, 1) and (2, -5), we have:
slope = (-5 - 1) / (2 - 4) = -6 / -2 = 3

So, the slope of the given segment is 3.

Step 3: Find the negative reciprocal of the segment's slope.
The negative reciprocal of a slope is obtained by flipping the fraction and changing the sign.

In this case, the negative reciprocal of 3 would be -1/3.

Step 4: Use the midpoint and the negative reciprocal slope to find the equation of the perpendicular bisector.
The equation of a line in point-slope form is given by:
y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, m is the slope of the line.

Using the midpoint (3, -2) as the point and the negative reciprocal slope -1/3, we have:
y - (-2) = -1/3(x - 3)
Simplifying, we get:
y + 2 = -1/3x + 1

Rearranging the equation and putting it in slope-intercept form y = mx + c:
y = -1/3x - 1

So, the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5) is y = -1/3x - 1.