I have a misunderstanding that at the moment I can't get clear in my mind, so any help would be appreciated

I am to find the

slope of a line.

I have two points (1,4) , (-6,5)

m = y2 - y1 / x2 - x1

m = 5 - 4 / -6 - 1

m = - 1/7

**<--- correct**
I am also asked to find the midpoint of the line.

A(x1 , y1), B(x2 , y2)

( 1/2 (x1 + x2) , 1/2(y1 + y2))

A = 1/2 (1 + (-6)) , B = 1/2 (4 + 5)

A = - 5/2 and B = 9/2

I am asked to find the

equation of

**the **bisector

**<--- there are an unlimited number of bisectors. You must be more clear here. I assume that you mean a perpendicular bisector(?)**
, this is where I get confused because I am not sure if the result below is to the original line and not the bisector?

Equation of the line

**<--- do you mean the line AB(?)**
y - y1 = m (x - x1)

y - 4 = - 7(x - 1)

**<--- if this should be AB then the slope is -1/7**
y - 4 = - 7x + 7

y = - 7x + 11

Now if I put the original "x" value into the equation y = - 7 (1) + 11, this yealds a result of 4, which is correct because it is the y

intercept above.

Now the problem.

If the perpendicular line

**<--- or do you mean the perpendicular bisector(?)**
, which is at 90 degrees to the original line has an opposite gradient, i.e.

perpendicular line is;

-1 / - 1/7 = 7

**<--- correct**
then using

y - y1 = m (x - x1)

we get

y - 4 = 7(x - 1)

y - 4 = 7x - 7

y = 7x - 7 + 4

y = 7x - 3

If I now plug in the "x" value above we get

y = 7(1) - 3

y = 4

There is absolutely nothing worse than fumbling around with scraps of paper trying and trying to get it right, thinking you have got it right, but then find you are suppose to use the midpoints AS fractions in your solutions, which is where I am now stuck?

Any help appreciated

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