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right-angled triangle, whose other vertex is at (x,y). What equation relates x

and y?

Attempt at solution:

So What I am thinking is that the line will be perpendicular to the line with end points 6,0 and 0,8.

So The gradient of this line is 4/3, hence the gradient of the other line perpendicular to this one will be -3/4

So the equation relating X and y is y = -3/4 x + c ?

Now can I assume that given line is a perpendicular bisector to the hypotenuse and so interesects it at 3,4 (mid point) and hence substitue for c - which i get to 25/4

So y = -3/4 x + 25/4 , This kinda feels wrong and I would appreciate input.

Thanks.