Final answer:
To find the equation of the perpendicular bisector of a line segment, first find the midpoint and then calculate the negative reciprocal of the slope. Substitute these values into the point-slope form to obtain the equation.
Step-by-step explanation:
To find the equation of the perpendicular bisector of a line segment, we need to find the midpoint of the line segment and the negative reciprocal of its slope.
The midpoint can be found by using the formula:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
For the given endpoints (2, 5) and (6, 11), the midpoint is (4, 8). Now, let's find the slope of the original line segment:
m = (y2 - y1)/(x2 - x1) = (11 - 5)/(6 - 2) = 1.5
The negative reciprocal of 1.5 is -2/3.
Now we have the slope and the midpoint, so we can use the point-slope form of a line to write the equation of the perpendicular bisector.
y - y1 = m(x - x1)Substitute the values: y - 8 = -2/3(x - 4)
This is the equation of the perpendicular bisector in point-slope form.