Find k which is a coordinate (k,4)

You can't use pythagoras for this one, you used it for the last one to find the length of ab which is root 41

No its not even that complicated you draw the triangle and then AC=AB so halfway is T (2,4) but I don't know how my teacher got here and full way is (2,8) you don't need to use that

Of course you can do it that way, but didn't you say earlier that you wanted to solve it through algebra?

not anymore haha thanks anyway :P

You don't necessarily have to find the equation of the line BC, you could just do:

$\displaystyle\frac{y_{B}-y_{C}}{x_{B}-x_{C}}=m_{BC}$

I mentioned that as well :G

I think it's actually slightly more complicated. I won't actually do the work for you but I think you merely know that it is a right angled triangle but do not know whether angle B is the right angle or C is the right angle. So you have to find the equation of the line AC using a gradient with Ks in it and similarly do this for the line BC. Then make X the subject of both equations and then solve a simultaneous equation substituting y in.

Similar question here shadab The point C has coordinates (2,t) where t>0, and AC=AB

A(7,4) B(2,0) C(2,t)
Equation of AB 4x-5y-8=0
I tried subbing in x as 2 but that didn't work! it made 5y=0 could you give me some guidance as to how to find t? thanks