SOLUTION: This problem is not in my book, my teacher likes to make up his own questions. I can't find anything on perpendicular bisector. I think it may have something to do with midpoint b

Question 82158: This problem is not in my book, my teacher likes to make up his own questions. I can't find anything on perpendicular bisector. I think it may have something to do with midpoint but I am not for sure. I would attempt it but I don't know where to begin...
Find an equation for the perpendicular bisector of the line segment IJ for the points I(3,5) and J(7,-3)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First find the midpoint of the segment with the endpoints (3,5) and (7,-3)

Solved by pluggable solver: To find midpoint of segment connecting two point

The Coordinates of mid point of a line segment joining two points can be calculated using following formulas.

X coordinate of mid point is

Y coordinate of mid point is

Hence, The mid point of segment joining two point (3,5) and (7,-3) is (5,1)

So we know that the bisecting line will go through the point (5,1). Now find the slope of the line going through (3,5) and (7,-3)

Solved by pluggable solver: Finding the slope

Slope of the line through the points (3, 5) and (7, -3)

Answer: Slope is

Since the slope of the line through (3,5) and (7,-3) is we know the perpendicular slope is
where is the perpendicular slope

So the bisecting line has a slope of 1/2 and goes through the point (5,1). So lets find the equation of the line:

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

it goes through point (5, 1)

it has a slope of 0.5

First, let's draw a diagram of the coordinate system with point (5, 1) plotted with a little blue dot:

Write this down: the formula for the equation, given point and intercept a, is

(see a paragraph below explaining why this formula is correct)

Given that a=0.5, and , we have the equation of the line:

Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: .

Here's the graph:

So the equation of the bisecting line is

or

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