1. **State the problem:** We have trapezium ABCD with vertices and a centre of enlargement X at (2,8). The trapezium is enlarged by a scale factor of 2 with centre X to get trapezium A'B'C'D'. We need to find the coordinates of vertex A'. 2. **Identify given points:** - Centre of enlargement, $X = (2, 8)$ - Vertex $A = (2, 6)$ 3. **Understand enlargement:** Enlarging a point $P$ with centre $X$ and scale factor $k$ means the vector from $X$ to $P$ is multiplied by $k$. 4. **Calculate vector from $X$ to $A$:** $$\vec{XA} = (2-2, 6-8) = (0, -2)$$ 5. **Multiply this vector by scale factor $2$:** $$2 \times \vec{XA} = 2 \times (0, -2) = (0, -4)$$ 6. **Find enlarged point $A'$ by adding the scaled vector to $X$ coordinates:** $$A' = X + 2 \vec{XA} = (2, 8) + (0, -4) = (2, 4)$$ 7. **Final answer:** The coordinates of vertex $A'$ are $\boxed{(2, 4)}$.