Solve the problem.
-Find all points $( x , y )$ with $x = y$ that are 5 units from $( 9,2 )$.
A) $( - 5 , - 5 )$ and $( - 6 , - 6 )$
B) $( - 5 , - 5 )$ and $( 6,6 )$
C) $( 5,5 )$ and $( - 6 , - 6 )$
D) $( 5,5 )$ and $( 6,6 )$

Question

Quizplus · Accepted Answer

The distance between any point $(x, y)$ and $(9, 2)$ is given by the distance formula: $\sqrt{(x - 9)^2 + (y - 2)^2} = 5$. Since $x = y$, we substitute $y$ with $x$ to get $\sqrt{(x - 9)^2 + (x - 2)^2} = 5$. Simplifying this equation will lead to two solutions for $x$ (and $y$), which are $x = 5$ and $x = 6$, thus the points are $(5,5)$ and $(6,6)$.

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