How do you find the equation that is the perpendicular bisector of the line segment with endpoints #(-2, 4)# and #(6, 8)#?

Answer 1

Equation of the perpendicular bisector: #y = -2x+10#

The slope of the line connecting these points must first be determined:

#m = (y_2-y_1)/(x_2-x_1) = (8-4)/(6-(-2)) = 4/8 = 1/2#
The line perpendicular to this will have #m = -2#

The midpoint's coordinates are also required.

#M((x_1+x_2)/2 ; (y_1+y_2)/2)#
#M((-2+6)/2 ; (4+8)/2)#
#M(2,6)#
Use the formula for slope and one point: #y-y_1 = m(x-x_1)#
#y -6 = -2(x-2)#
#y = -2x+4+6#
Equation of the perpendicular bisector: #y = -2x+10#
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Answer 2

To find the equation of the perpendicular bisector of a line segment with endpoints (2,4)(-2, 4) and (6,8)(6, 8), follow these steps:

  1. Find the midpoint of the line segment using the midpoint formula:
(x1+x22,y1+y22)\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)
  1. Determine the slope of the line segment using the slope formula:
m=y2y1x2x1m = \frac{{y_2 - y_1}}{{x_2 - x_1}}
  1. Find the negative reciprocal of the slope calculated in step 2 to get the slope of the perpendicular bisector.
  2. Use the midpoint found in step 1 and the slope from step 3 in the point-slope form of the equation of a line:
yy1=m(xx1)y - y_1 = m(x - x_1)
  1. Simplify the equation obtained in step 4 to its standard form, if required.

Following these steps, you can find the equation of the perpendicular bisector of the line segment.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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