Answer
Yes, ($-\frac{24}{25},-\frac{7}{25}$) is a point on the unit circle.
Work Step by Step
Since ($-\frac{24}{25},-\frac{7}{25}$) is an (x, y) coordinate we can plug it into the equation of a circle, $x^{2}+y^{2}=1$.
$$(-\frac{24}{25})^{2}+(-\frac{7}{25})^{2}=1$$ $$\frac{-24\times-24}{25\times25}+\frac{-7\times-7}{25\times25}=1$$ $$\frac{576}{625}+\frac{49}{625}=1$$ $$\frac{625}{625}=1$$ We end up with 1=1, which is true. Therefore, ($-\frac{24}{25},-\frac{7}{25}$) is a point on the unit circle.