what is the equation for the perpendicular bisector of the line segment between points A(2,5) and B(-6,-1)?

Answer 1

The perpendicular bisector will have a slope equal to the negative reciprocal of AB's slope, and also pass through the midpoint of AB.

Find the slope of AB:

Slope = (y2 - y1) / (x2 - x1)
Slope = (-1 - 5) / (-6 - 2)
Slope = -6 / -8
Slope = 3 / 4

Therefore the slope of the perpendicular bisector will be -4/3

Find the midpoint of AB:

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2))
Midpoint = ((2 + (-6)) / 2), ((5 + (-1)) / 2))
Midpoint = ((-4/2), (4/2))
Midpoint = (-2, 2)

Write the equation in slope - y intercept form, and find the y intercept by plugging the midpoint into the equation:

y = (-4/3) x + b
2 = (-4/3) (-2) + b
2 = 8/3 + b
b = -2/3

Therefore the equation of the line in slope - y intercept form is

y = (-4/3) x - 2/3

Or in standard form:

3y = -4x - 2
3y + 4x = -2

Answer 2

Perpendicular Bisector Of A Segment

Answer 3

A perpendicular bisector has to be two things:
1) perpendicular
2) a bisector
simple enough.
for the perpendicular find the slope from A to B then its opposite reciprocal
(5 - -1)/(2 - -6) = 6/8 = 3/4 so the perpendicular slope is -4/3
for the bisector find the midpoint from A to B by averaging the coordinates
(2+-6)/2 = -2
(5+-1)/2 = -2
so the midpoint is (-2,-2)

So the perpendicular bisector in point-slope form is
y+2 = -4/3 (x+2)

Answer 4

How To Find Perpendicular Bisector

Answer 5

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mx = (-2 + 10) / 2 mx = 8/2 mx = 4 my = (-4 + 6) / 2 my = 2 / 2 my = 1 (4, 1) is the midpoint of the segment AB slope of AB m = (6 - (-4)) / (10 - (-2)) m = (6 + 4) / (10 + 2) m = 10/12 m = 5/6 slope of perpendicular line is -6/5 going through point (4, 1) y - 1 = (-6/5)(x - 4) y - 1 = (-6/5)x + 24/5 y = (-6/5)x + 29/5 [slope intercept form] 5y = -6x + 29 6x + 5y = 29 [standard form]

Answer 6

Slope of line segment AB is 3/4. So gradient of perpendicular bisector is -4/3. Bisector passes through midpoint of AB at (-2,2)

y = m x +c

2 = -4 x/3 + c

Solve for c

c= 2/3 (2x + 3)

Substitute x = -2

c = -2/3

Equation of bisector is y = (-4 x/3) - 2/3

Answer 7

Assume that the point A is (x1, y1) and B is (x2, y2). First, find the midpoint between A and B, which would be ((x1 + x2)/2, (y1 + y2)/2), because the bisector must pass through this point. Then, find the slope between A and B, using the formula m = (y1 - y2) / (x1 - x2), where the points A and B are (x1, y1) and (x2, y2). Next, take the opposite reciprocal of this slope, i.e., -1/m, because perpendicular lines have opposite reciprocal slopes. Finally, take the slope of the perpendicular bisector and the known point it passes through--call it (h, k)--and formulate the point-slope formula for the equation of a line: y - k = (-1/m)(x - h), where -1/m takes the place of the normal m to represent the slope of the line, because we used m to represent the other slope we calculated.

Answer 8

what are the perpendicular bisectors of these lines?