Question

Indicate the equation of the given line in standard form, writing the answer below.

The line that is the perpendicular bisector of the segment whose endpoints are R(-1,6) and S(5,5).

Answer 1

Answer:
`y-(11)/(2)=6(x-2)`

Explanation:

For it to bisect the segment, we need to find the midpoint.

The midpoint is
`\left((-1+5)/(2), (6+5)/(2) \right)=\left(2, (11)/(2) \right)`.

Now, for it to be perpendicular, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the given segment is
`(6-5)/(-1-5)=-(1)/(6)`, so the slope of the perpendicular bisector is 6.

Thus, the equation of the line in point-slope form is
`\boxed{y-(11)/(2)=6(x-2)}`