Press a button to move the triangle. The dashed shape is the original triangle; the solid shape is the moved triangle. See exactly what rule the coordinates follow for each kind of move.
Reflection is easiest to picture as a mirror image. Flip across the x-axis (using it as the mirror) and only up-and-down flips, so only the y-coordinate's sign changes. Flip across the y-axis and only left-and-right flips, so only the x-coordinate's sign changes. Reflecting through the origin is like applying both mirrors at once, so both x and y flip sign — which, it turns out, gives exactly the same result as a 180° rotation.
Translation is simply picking the whole shape up and setting it down somewhere else. The shape and orientation never change at all — only the position shifts by dx and dy.
Rotation spins the shape counterclockwise around the origin. Every 90° turn swaps x and y with each other, flipping one sign each time — a rule that repeats itself. Press the 90°, 180°, and 270° buttons in order and watch how this rule keeps repeating.