Coordinates of a symmetrical figures in a coordinate system

Question

Let's say that I have a triangle with vertexes (0, 0), (0.5, 1), (1, 0). I need to find a coordinates of a point symmetrical or a line symmetrical triangle. But how do I calculate that without drawing? For example, the line is y=1.5 or a point is (0.5, 1.5). I know that coordinates of a new triangle should be (0, 3), (0.5, 2), (1, 3), but are there any formulas to find it? I know $\frac {y - v}{x - u}\times a$ and $x^2 + (y - b)^2 = u^2 + (v - b)^2$ but they didn't work for me. Thank you in advance!