Question

Indicate in standard form the equation of the line given the following information: the line that is the perpendicular bisector of the segment whose endpoints are r(-1, 6) and s(5, 5)

a. 12x - 2y = 13
b. 2x - 12y = -13
c. -2x + 12y = 13
d. -12x + 2y = -13

Answer 1

To find the equation of the perpendicular bisector of the segment with endpoints R(-1, 6) and S(5, 5), we can find the midpoint and the slope of the perpendicular bisector. The midpoint is (2, 11/2) and the slope of the perpendicular bisector is 6. Therefore, the equation of the line is y = 6x - 23.

Step-by-step explanation:

To find the equation of the line that is the perpendicular bisector of the segment with endpoints R(-1, 6) and S(5, 5), we need to find the midpoint of the segment and then determine the slope of the perpendicular bisector. The midpoint of the segment is [(x1 + x2)/2, (y1 + y2)/2] = [(5 - 1)/2, (5 + 6)/2] = [2, 11/2].

The slope of the line passing through points R and S is (y2 - y1)/(x2 - x1) = (5 - 6)/(5 - (-1)) = -1/6. The slope of a line perpendicular to this line is the negative reciprocal of -1/6, which is 6. So, the equation of the perpendicular bisector is y - (11/2) = 6(x - 2).

Simplifying the equation, we get y = 6x - 23.