Question 751147
1.Get a piece of graph paper.  

2.Plot the point (4,-3).

3.Draw a horizontal line from (4,-3) connecting to the y-axis at the point (0,-3)

4.The line forms right angles with the y-axis and it's length is 4. 

5.Now if you form a right triangle by drawing another line from point (4,-3) and connecting to the y-axis.  The coordinates of where it connects to the y-axis will be (0, -3+a) and (0, -3-a).  We are going to find a using the Pythagorean theorem, with b=4 and c=6.    

{{{a^2+b^2=c^2}}}

{{{a^2+4^2=6^2}}}

{{{a^2+16=36}}}

{{{a^2=20}}}

{{{a= sqrt(20)}}}

{{{a= sqrt(4)*sqrt(5)}}}

{{{a=2sqrt(5)}}}

The coordinates on the y-axis that are 6 units from (4,-3) are (0, -3+2sqrt(5)) and (0, -3-2sqrt(5))