Let , coordinate of points are P( h,k ).
Also , k = 3h + 1
Distance of P from origin :
[tex]d=\sqrt{h^2+k^2}[/tex]
Distance of P from ( -3, 4 ) :
[tex]d=\sqrt{(h+3)^2+(k-4)^2}[/tex]
Now , these distance are equal :
[tex]h^2+(3h+1)^2=(h+3)^2+(3h+1-4)^2\\\\h^2+(3h+1)^2=(h+3)^2+(3h-3)^2[/tex]
Solving above equation , we get :
[tex]P=(\dfrac{16}{21},\dfrac{23}{7})[/tex]
Hence , this is the required solution.
