please help, point on the x-axis and y-axis that = equidist

[nigel]

please help find the coordinates of the point on the 1. x-axis that is equidistant from each pair of points and 2. y-axis that is equidistant rom each pair of points

Question: R(5,5) and S(4,-4)

answer part 1. (9,0)

answer part 2. (0,1)

When I graphed the question I understood why the answers are correct, but I don't understand how to get the answers. Please help me out. If someone could explain how to do this question, I will be able to finish similar questions in my homework.

Thanks!

 

[galactus]

Use the distnace formula and solve for x.

Since the point is on the x-axis, the y-coordinate will be 0.

\(\displaystyle \L\\\sqrt{(5-x)^{2}+(5-0)^{2}}=\sqrt{(4-x)^{2}+(-4-0)^{2}}\)

Do the same for the y-axis problem.

 

[pka]

Suppose that (0,b) is the point on the y-axis then:
\(\displaystyle \L
\sqrt {\left( {0 - 5} \right)^2 + \left( {b - 5} \right)^2 } = \sqrt {\left( {0 - 4} \right)^2 + \left( {b + 4} \right)^2 }.\)
Now solve for b.

 

[nigel]

Thanks

Thank You both galactus and pka