SOLUTION: I've checked all over this site, but can't find a response for these 2 problems. Please help! 1.Find the coordinates of the point C, halfway between the points A(5,1) and B(-2,

Question 168522: I've checked all over this site, but can't find a response for these 2 problems.
Please help!
1.Find the coordinates of the point C, halfway between the points A(5,1) and B(-2,7).
2. What is the equation of the perpendicular bisector of teh line between the points (2,2) and (6,6)?
Thanks in advance for any help!
Andrew
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I've checked all over this site, but can't find a response for these 2 problems.
Please help!
1.Find the coordinates of the point C, halfway between the points A(5,1) and B(-2,7).
---------------
The easiest way to do these is to find the average of x and y separately.
A(5,1) and B(-2,7).
For x: (5 + (-2))/2 = 3/2
For y: (1+7)/2 = 4
So the point is (3/2,4) or (1.5,4)
-------------------------
2. What is the equation of the perpendicular bisector of teh line between the points (2,2) and (6,6)?
The mid-point is found in the same way as above, and is (4,4).
The slope of the line is the (diff in y)/(diff in x) = 1
The slope, m, of a line perpendicular is the negative inverse, = -1.
Then,
y-y1 = m*(x-x1) where (x1,y1) is the point (4,4)
y-4 = -1(x-4)
y-4 = -x + 4
x+y = 8

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

X-coordinate of the midpoint: average of the two x coordinates

x-mid = (5+(-2))/2 = 3/2 = 1.5

Y-coordinate of the midpoint: average of the two y coordinates

y-mid = (1+7)/2 = 8/2 = 4

Midpoint between the points A(5,1) and B(-2,7): (1.5, 4)

Note: you can graph the points and measure the distances to verify

# 2

Use the same technique used in problem #1 to get the midpoint (4, 4)

Now find the slope between the the points (2,2) and (6,6)

Whatever that slope turns out to be, find the reciprocal (ie flip the fraction) and change the sign to find the perpendicular slope. For instance if the slope is 1/2, then flip and change the sign to get -2/1.

Once you have the perpendicular slope, plug it into the equation

where in this case is the perpendicular slope and is the midpoint

From there, solve for "y" to find the equation of the perpendicular bisector

Feel free to ask for further help in finding the perpendicular bisector.
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