find all the points having a x-coordinate of 2 whose distance from the point (-2, -1) is 5.

Question

solomonzelman · Answer

add 5 to the y coordinate   
OR
subtract 5 from the y coordinate

anonymous · Answer

Slightly more in-depth approach: Any point with an x-coordinate of 2 will have the form $(2,y)$.

The distance between such a point and $(-2,-1)$ is
$$d=\sqrt{(2-(-2))^2+(y-(-1))^2}$$
Given that $d=5$, you can solve for $y$:
$$\begin{align*}5&=\sqrt{(2-(-2))^2+(y-(-1))^2}\
25&=4^2+(y+1)^2\
9&=(y+1)^2\
\pm3&=y+1\
y&=-1\pm3
\end{align*}$$

solomonzelman · Answer

yeah, just a tiny bit deeper....

anonymous · Answer

@SolomonZelman I just noticed this... Adding/subtracting 5 to the given point's y-coordinate won't work because we're using $(-2,-1)$, which does not lie on the line $x=2$:
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