The coordinates of a vertex after a translation 2 units right and reflection across x = 0 are found by first adding 2 to the original x-coordinate and then taking the opposite of this result. The y-coordinate remains unchanged throughout both transformations.
To find the coordinates of a vertex after a translation followed by a reflection, we first apply the translation. When translating a point 2 units to the right, we add 2 to the x-coordinate, leaving the y-coordinate unchanged. If the original coordinates of the vertex are (x, y), after the translation, they would become (x+2, y).
Next, we reflect the point across the line x = 0. A reflection across x = 0 switches the sign of the x-coordinate but leaves the y-coordinate the same. Therefore, the new x-coordinate becomes -(x+2). The final coordinates after both transformations would be (-(x+2), y).
Remember, when calculating changes in positions (the displacement), the formula is ∆x = x1 - xo, which indicates the final value minus the initial value.