You can
put this solution on YOUR website!What is the equation of the perpendicular bisector of the line between the points (2,2) and (6,6)?
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Find the point. The easiest way (always use the easiest) is to average x and y separately
(2+6)/2 = 4 (x and y in this case)
The mid-point is (4,4)
Now find the slope, m
m = diffy/diffx
m = (6-2)/(6-2)
m = 1
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The slope of lines perpendicular (there are an infinite number of them) have a slope that's the negative inverse.
m2 = -1
Then use
y-y1 = m2*(x-x1) where (x1,y1) is (4,4)
y-4 = -1(x-4)
y-4 = -x+4
x+y = 8
You can
put this solution on YOUR website!Step 1) First find midpoint of the points (2,2) and (6,6)
To find the midpoint, first we need to find the individual coordinates of the midpoint.
X-Coordinate of the Midpoint:
To find the x-coordinate of the midpoint, simply average the two x-coordinates of the given points by adding them up and dividing that result by 2 like this:
So the x-coordinate of the midpoint is
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Y-Coordinate of the Midpoint:
To find the y-coordinate of the midpoint, simply average the two y-coordinates of the given points by adding them up and dividing that result by 2 like this:
So the y-coordinate of the midpoint is
So the midpoint between the points
)
and
)
is
)
=======================================================
Step 2) Find the slope of the line through the points (2,2) and (6,6)
Note:
)
is the first point
and
)
is the second point
.
Start with the slope formula.
Plug in
,
,
, and
Subtract
from
to get
Subtract
from
to get
Reduce
So the slope of the line that goes through the points
and
is
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Step 3) Find the perpendicular slope
Take the slope
and flip the fraction (think of it as
) to get
and change the sign to get
. So the perpendicular slope is
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Step 4) Find the equation of the line with the perpendicular slope (found in step 3) which goes through the midpoint (found in step 1)
To recap, the perpendicular slope is
and the point that the perpendicular bisector goes through is (4,4)
So let's find the equation of the line with a slope
and goes through the point (4,4)
If you want to find the equation of line with a given a slope of
which goes through the point (
,
), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
where
is the slope, and
)
is the given point
So lets use the Point-Slope Formula to find the equation of the line
Plug in
,
, and
(these values are given)
Distribute
Multiply
and
to get
Add 4 to both sides to isolate y
Combine like terms
and
to get
So the equation of the line with a slope of
which goes through the point (
,
) is:
which is now in
form where the slope is
and the y-intercept is
==============================================================
Answer:
So the equation of the perpendicular bisector of the line between the points (2,2) and (6,6) is
So the answer you're looking for is
Here's the graph to verify the answer:
(