How do you find the equation of the perpendicular bisector of the points #(1,4)# and #(5,-2)#?

Answer 1

#y=2/3x-1#

#"a perpendicular bisector, bisects a line segment at"# #"right angles"#
#"to obtain the equation we require slope and a point on it"#
#"find the midpoint and slope of the given points"#
#"midpoint "=[1/2(1+5),1/2(4-2)]#
#color(white)("midpoint ")=(3,1)larrcolor(blue)"point on bisector"#
#"calculate the 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)=(1,4)" and "(x_2,y_2)=(5,-2)#
#rArrm=(-2-4)/(5-1)=(-6)/4=-3/2#
#"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/(-3/2)=2/3larrcolor(blue)"slope of bisector"#
#"using "m=2/3" and "(x_1,y_1)=(3,1)" then"#
#y-1=2/3(x-3)larrcolor(red)"in point-slope form"#
#rArry-1=2/3x-2#
#rArry=2/3x-1larrcolor(red)"in slope-intercept form"#
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Answer 2

To find the equation of the perpendicular bisector of the line segment between the points ((1, 4)) and ((5, -2)):

  1. Find the midpoint of the line segment using the midpoint formula: [ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]

  2. Calculate the slope of the line passing through the two given points using the slope formula: [ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ]

  3. Determine the negative reciprocal of the slope found in step 2 to obtain the slope of the perpendicular bisector.

  4. Use the midpoint found in step 1 and the slope obtained in step 3 to write the equation of the perpendicular bisector using the point-slope form: [ y - y_1 = m_{\text{perpendicular}}(x - x_1) ]

  5. Simplify the equation to obtain the final form.

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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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