Finding the equation of a perpendicular bisector

[Probability]

I am really struggling to solve a problem which to most would probably seem simple, however with reference to the graph I am asked to find the midpoint, which I found by saying 1//2(x1 + x2), 1/2(y1 + y2). I came up with midpoints of;

x midpoint = -5/2

y midpoint = 9/2

My graph has a gradient of -1/7

From this point I am asked to find the equation of the perpendicular bisector AB

I have looked at the only given example in the coursebook and must say that to me it is very unclear, even the fractions they use when worked out don't equate to the same answer they give?

So either I am not understanding or the book has a mistake that I cannot get my head round and is stopping me understanding this problem of finding this equation?

Any help much appreciated.

 

[wjm11]

Your sketch is of little help since one cannot read any values on it. However, let us assume that you found the midpoint correctly: (-5/2, 9/2). You also listed the slope as -1/7. The perpendicular bisector must have a slope that is the negative reciprocal of this value, so its slope is 7. You now have a point (-5/2) and a slope (7). This is sufficient information to define a line. Can you write the equation with this information?

 

[Probability]

Your sketch is of little help since one cannot read any values on it. However, let us assume that you found the midpoint correctly: (-5/2, 9/2). You also listed the slope as -1/7. The perpendicular bisector must have a slope that is the negative reciprocal of this value, so its slope is 7. You now have a point (-5/2) and a slope (7). This is sufficient information to define a line. Can you write the equation with this information?

I have no idea when this is right or not, but;

y + 9/2 = - 1/7(x - 5/2)

????

 

[srmichael]

I have no idea when this is right or not, but;

y + 9/2 = - 1/7(x - 5/2)

????

Nope. Point-Slope form is y-y1 = m(x-x1).

You have a point (-5/2,9/2) and, like wjm11 said, you have a slope of 7.

Now try.

 

[Probability]

Nope. Point-Slope form is y-y1 = m(x-x1).

You have a point (-5/2,9/2) and, like wjm11 said, you have a slope of 7.

Now try.

I won't be able to use the information you give above, the reasons are that the book I have shows y = mx + c, where you are showing a derivative of such and my book does not show the steps involved to get from one to the other, and the book does not explain y - y1 or x - x1?

What I mean is this;

which comes first x or x1?

Why is it not x1 - x2, or x2 - x1?

How can you have y - y1?

The book I have does not say that y is y2 yet it can't be y1, so I can't follow through?

On my last maths course I have religiously followed through the information and this information above you present, which is also in my book is now new information, which has not been explained to me in my course books from the past or present, so I am absolutely at a loss how I am supposed to learn something from nothing?

Please don't think I am having a go at you because I am not, it's just the written material that somebody thought was good is absolutely terrible and desiged to put a student in a blind bend everytime you turn the corner?

 

[Mrspi]

Well, ok....if what the other responders have posted is "new iinformation" which you have not seen before, let's work with what you SAY your do know.

y = mx + c

This is called "slope-intercept" form for the equation of a line with slope m and y-intercept c.



Your perpendicular bisector has slope 7, right? (See the previous posts for explanation of that fact.)

So, we could AT LEAST say that the equation must be
y = 7x + c
However, we don't yet know the y-intercept, so we have no value to substitute for "c".

The perpendicular bisector must go through the midpoint, which you've said is (-9/2, 5/2). I didn't check to see if that is accurate.......I'll assume you've done that part correctly.

So....if the point (-9/2, 5/2) is to be ON the perpendicular bisector, our equation

y = 7x + c

must be TRUE when x = -9/2 and y = 5/2. Substitute those values for x and y:

5/2 = 7(-9/2) + c

That equation has just one variable, "c." Let's solve it for c. Start by doing the multiplication on the right side. 7*(-9/2) is the same thing as (7/1)*(-9/2), which is -63/2

5/2 = (-63/2) + c

Add 63/2 to both sides of the equation:

(5/2) + (63/2) = (-63/2) + c + (63/2)

68/2 = c
34 = c

NOW we can finish the equation....we had
y = 7x + c
And we know that c = 34.
y = 7x + 34

There is often more than one way to accomplish a task....

 

[Probability]

I must thank you for putting the time in to help solve my problem. I know you assumed some of my calculations are correct to reach your answers, so any errors are my fault.

I have followed your logic to the solution and I have tried to use the coordinates and equation to find the value of y, however I am somewhat confused because looking at my graph the gradient of 1/-7 with a midpoint of -5/2 in my workings seems to give a y value of 29. I am confused by my answer and yours because if you look at the graph the bisector actually at 90 degrees to the line AB goes downwards in the negative direction and would represent the radius of a circle, therefore I cannot see how it would ever intercept the y axis, and again this is another major part of my confusion, which again cannot be answered by google?

I would have thought that following your line of reasoning above that once I know the values of the coordinates and the gradient that I should be able to plug them into the equation and find the value of C, then plug that value back into the equation and find the y value, which is where everything falls apart because the bisector should be within the circle and not outside going upwards?

Thanks for the help recieved.