State True or False. Coordinates of three points are $$A(-3, 2)$$, $$B(25, 10)$$, $$C(k, k)$$. If the value of $$AC + BC$$ is minimum then $$k = 6$$.

$$C$$ lies on the line $$y = x$$, and $$A$$ and $$B$$ are on opposite sides of it ($$2 > -3$$ but $$10 < 25$$). So $$AC + BC$$ is least when $$C$$ is where segment $$AB$$ crosses $$y = x$$. Line $$AB$$ is $$y - 2 = \frac{2}{7}(x + 3)$$; putting $$y = x$$ gives $$5x = 20$$, so $$k = 4$$, not 6. The statement is False.