Question

A(1,3) B(-3,5)

find the perpendicular bisector equation

Answer 1

i know the slope is -2

Answer 2

Find the midpoint also, the perpendicular line will pass through this point.

Answer 3

the midpoint is -1,4

Answer 4

So can you write an equation for a line that passes through (-1,4) with a slope of 1/2?

Answer 5

so it would be
y-4 = 1
x-(-1) = 2 ?

Answer 6

if slope is -2 of the original line given two vertices,therefor the slope of the perpendicular line is 1/2

Answer 7

the answer is 2x - y = -6
but i get a different answer

Answer 8

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
\[y-2x+6\]

Answer 9

\[ y-2x=6\]

Answer 10

or it can be written as \[2x-y=-6\]

Answer 11

isnt the mid point (-1,4)?

Answer 12

1 + (-3) = -2
then -2 / 2 = -1

Answer 13

since the question is the perpendicular bisector equation of the line, we will be needing the midpoint and the perpendicular slope. .

Answer 14

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:)

Answer 15

nikkyster if you got the slope to =2, you calculated the slope wrong

Answer 16

The slope of the original line is -1/2

Answer 17

i got the slope to be -2

Answer 18

yeah slope of line is \[-\frac{1}{2}\]

Answer 19

I should've double checked it earlier ;p

Answer 20

But you have the right midpoint

Answer 21

yeah your right ! i got the slope wrong

Answer 22

what about for midpoint with a decimal?

Answer 23

therefor the perpendicular slope is 2, the equation of the perpendicular line is