Equation of a perp bisector (help)

Question) write an equation of the perp bisector of AB whose points are A (8,-2) and B (4,4)

so i sketched the the two points, found the midpoint which is (6,1)
then found the gradient which is difference of y divided by difference of x and I got -3/2

the perp gradient is 2/3

the equation of the perp biscector: y-1 = 2/3 (x-6)
I x by 3 to get rid of the fraction
and i got 3y-3 = 2x - 12

this question never said to rearrange in the form ax _ by _ c = 0
but I didn't know what to do?

the answer comes up as y= 2/3x - 3

You've got it right, it's just that normally line equations are written in the form, y=mx+c or ax+by+c=0.

ok so if I did in the form ax+by+c=0

would by answer be -2x+3y+9=0?

Question) write an equation of the perp bisector of AB whose points are A (8,-2) and B (4,4)

so i sketched the the two points, found the midpoint which is (6,1)
then found the gradient which is difference of y divided by difference of x and I got -3/2

the perp gradient is 2/3

the equation of the perp biscector: y-1 = 2/3 (x-6)
I x by 3 to get rid of the fraction
and i got 3y-3 = 2x - 12

this question never said to rearrange in the form ax _ by _ c = 0
but I didn't know what to do?

the answer comes up as y= 2/3x - 3

Yes.

Your working isn't wrong. Only thing is that you haven't simplified your equation as much as you can, which you normally want to do.

The perpendicular bisector is going to be a line, so it will have a corresponding equation.

If I gave you an equation of a line and told you it was (y - c) / m = x, it wouldn't be of much use would it?

You have the equation, but it is not in the usual forms which you would normally want (y = mx + c or ax + by + c = 0). These forms are chosen because y = mx + c lets you clearly see some important properties of the line (m being the gradient, c being the y intercept), and ax + by + c = 0 because you have everything on one side and you can easily rearrange for anything you want such as the gradient or y intercept.

Also, ax + by = c is sometimes generally used.

Your working isn't wrong. Only thing is that you haven't simplified your equation as much as you can, which you normally want to do.

The perpendicular bisector is going to be a line, so it will have a corresponding equation.

If I gave you an equation of a line and told you it was (y - c) / m = x, it wouldn't be of much use would it?

You have the equation, but it is not in the usual forms which you would normally want (y = mx + c or ax + by + c = 0). These forms are chosen because y = mx + c lets you clearly see some important properties of the line (m being the gradient, c being the y intercept), and ax + by + c = 0 because you have everything on one side and you can easily rearrange for anything you want such as the gradient or y intercept.

Also, ax + by = c is sometimes generally used.

thanks

just out of interest, if i was to rearrange in the form y=mx + c

what do i do from this? y-1 = 2/3 (x-6)

I don't x by 3 do i?

do I do 2/3x and then times 2/3 x -6
and then plus 1 to get y= 2/3x - 3 ?

P.s this is c1, so i can't use a calc how do i do 2/3 x -6 ?

You can do it that way.
Easiest way is to multiply by 3. so you have 3y-3 = 2x-12
then add 3 to both sides: 3y=2x-9
then divide by 3: y=2/3x -3

It doesn't matter how you rearrange as long as it's correct and all comes to the same answer.

got it thanks