How do you find the equation for the perpendicular bisector of the segment with endpoints #(-1,-3)# and #(7,1)#?

Answer 1

#y=-2x+5#

#"the perpendicular bisector bisects the line segment at"# #"right angles"#
#"we require to find the midpoint of the segment and "# #"the slope m"#
#"the midpoint of any endpoints say "(x_1,y_1)" and "(x_2,y_2)" is"#
#•color(white)(x)[1/2(x_1+x_2),1/2(y_1+y_2)]#
#"midpoint "=[1/2(-1+7),1/2(-3+1)]#
#color(white)("midpoint ")=[1/2(6),1/2(-2)]=(3,-1)#
#"calculate slope m using the "color(blue)"gradient formula"#
#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#
#"let "(x_1,y_1)=-1,-3)" and "(x_2,y_2)=(7,1)#
#rArrm=(1-(-3))/(7-(-1))=4/8=1/2#
#"given a line with slope m then the slope of a line"# #"perpendicular to it is"#
#•color(white)(x)m_(color(red)"perpendicular")=-1/m#
#rArrm_"perpendicular"=-1/(1/2)=-2#
#"the equation of a line in "color(blue)"point-slope form"# is.
#•color(white)(x)y-y_1=m(x-x_1)#
#"where m is the slope and "(x_1,y_1)" a point on the line"#
#"using "m=-2" and "(x_1,y_1)=(-1,-3)" then"#
#rArry+1=-2(x-3)larrcolor(red)"in point-slope form"#
#rArry+1=-2x+6#
#rArry=-2x+5larrcolor(red)"in slope-intercept form"#
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Answer 2

To find the equation for the perpendicular bisector of the segment with endpoints ((-1,-3)) and ((7,1)), follow these steps:

  1. Find the midpoint of the segment by averaging the coordinates of the endpoints.
  2. Determine the slope of the segment by using the formula (m = \frac{{y_2 - y_1}}{{x_2 - x_1}}).
  3. Find the negative reciprocal of the slope of the segment to get the slope of the perpendicular bisector.
  4. Use the midpoint coordinates and the slope of the perpendicular bisector to write the equation of the line in point-slope form.
  5. Optionally, simplify the equation into slope-intercept form if desired.
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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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