A(1,3) B(-3,5) find the perpendicular bisector equation

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A(1,3) B(-3,5) find the perpendicular bisector equation

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i know the slope is -2
Find the midpoint also, the perpendicular line will pass through this point.
the midpoint is -1,4

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So can you write an equation for a line that passes through (-1,4) with a slope of 1/2?
so it would be y-4 = 1 x-(-1) = 2 ?
if slope is -2 of the original line given two vertices,therefor the slope of the perpendicular line is 1/2
the answer is 2x - y = -6 but i get a different answer
We have the line connecting the points A(1,3) and B(-3,5) the point which divides the line into two halves will have coordinates D(x1,y1) \[ x1= \frac{1+(-3)}{2}\] and \[y1=\frac{3+5}{2}\] so we get \[(x1,y1= (-2, 4)\] so the perpendicular bisector will pass through this point and we need one more condition like another point or slope to find out its equation here it's easy to find the slope of perependicular bisector Let the slope of AB be m1 and of the perpendicular bisector be m2 \[m1= \frac{5-3}{-3-1}\] we get \[m1= -\frac{1}{2}\] now since AB and its perpendicular bisector are perpendicular to each other \[ m1*m2=-1\] so \[m2=2\] so we have the slope m2= 2 and the line passes through D(-2, 4) so equation will be \[ \frac{y-4}{x+2}= 2\] so we get \[y-4=2x+2\] so the equation is \[y-2x+6\]
\[ y-2x=6\]
or it can be written as \[2x-y=-6\]
isnt the mid point (-1,4)?
1 + (-3) = -2 then -2 / 2 = -1
since the question is the perpendicular bisector equation of the line, we will be needing the midpoint and the perpendicular slope. .
sorry I made a mistake then you'll get \[ \frac{y-4}{x+1}=2\] or \[y-4=2x+2\] or \[y-2x=6\] i made mistake 2 times and fortunately got the correct answer:)
nikkyster if you got the slope to =2, you calculated the slope wrong
The slope of the original line is -1/2
i got the slope to be -2
yeah slope of line is \[-\frac{1}{2}\]
I should've double checked it earlier ;p
But you have the right midpoint
yeah your right ! i got the slope wrong
what about for midpoint with a decimal?
|dw:1328422479768:dw||dw:1328422542891:dw||dw:1328422687105:dw| therefor the perpendicular slope is 2, the equation of the perpendicular line is
|dw:1328422920367:dw|
A(3,1) B(-3,6)
the midpoint is (0,3.5) and the slope would be -5/6
is this another problem?
yes
what's the question? prependicular equation?
perpendicular ?

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