Question

find two choices for t such that the distance between (3,-2) and (1,t) equals 5

Answer 1

What I would do is use the distance formula
\[s=\sqrt{(x _{2}}-x _{1})^2+(y _{2}-y _{1})^2\]

we are given two coordinates
(3, -2) and (1,t)
\[(x _{1},x _{2})(y _{1},y _{2})\]

lets sub it in:
\[5=\sqrt{(-2-3)+(t-1)}\]
\[5=\sqrt{-5+(t-1)}\]
\[5=\sqrt{-6+t}\]

Now solve for t