A line segment starts at the point (2,3) and ends at the point (6,11). Find the equation of the perpendicular bisector of the segment. Demonstrate that your answer is correct. Your equation must be written in slope intercept form.

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PrObLemOcCuReD PrObLemOcCuReD · Answer 1 · 2020-08-26T01:39:30+02:00

1). Slope = (-2)

2). Midpoint = (2, -2)

3). Slope of the perpendicular bisector = (1/2)

4). Equation of perpendicular bisector will be x - 2y = 6

Step-by-step explanation:

A line segment has the endpoints at (4, -6) and (0, 2).

1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)

2). Mid point of the line segment is given by

Therefore midpoints of the line segment will be = (2, -2)

3). Slope of the perpendicular bisector is represented by

⇒ (-2)×m2 = (-1)

⇒

4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).

Since standard equation of the line will be given as y = mx + c

passes through (2, -2).

c = (-1) - 2 = -3

Finally the equation of perpendicular bisector will be

⇒ 2y = x - 6

⇒ 2y - x = -6

⇒ x - 2y = 6