Question: C is the centre of rectangle DEFG.
Work out the coordinates of G.
D is at the top-left of the rectangle, E is at the top-right and is labeled $(20, 25)$, C is the centre and is labeled $(8, 7)$, and G is the bottom-left vertex in the bottom-left area of the graph.
1. **State the problem:** We need to find the coordinates of point $G$, the bottom-left vertex of rectangle $DEFG$, given that $C$ is the center of the rectangle, $D$ is the top-left vertex, and $E$ is the top-right vertex with coordinates $(20, 25)$, and $C$ has coordinates $(8, 7)$.
2. **Recall the properties of a rectangle and its center:** The center $C$ of a rectangle is the midpoint of the diagonal connecting opposite vertices. Here, $C$ is the midpoint of diagonal $EG$ and also of diagonal $DF$.
3. **Use the midpoint formula:** The midpoint $C$ of points $E(x_E, y_E)$ and $G(x_G, y_G)$ is given by:
$$
C = \left( \frac{x_E + x_G}{2}, \frac{y_E + y_G}{2} \right)
$$
4. **Substitute known values:** We know $C = (8, 7)$ and $E = (20, 25)$, so:
$$
8 = \frac{20 + x_G}{2} \quad \Rightarrow \quad 2 \times 8 = 20 + x_G \quad \Rightarrow \quad 16 = 20 + x_G
$$
$$
7 = \frac{25 + y_G}{2} \quad \Rightarrow \quad 2 \times 7 = 25 + y_G \quad \Rightarrow \quad 14 = 25 + y_G
$$
5. **Solve for $x_G$ and $y_G$:**
$$
x_G = 16 - 20 = \cancel{16} - 20 = -4
$$
$$
y_G = 14 - 25 = \cancel{14} - 25 = -11
$$
6. **Conclusion:** The coordinates of $G$ are $(-4, -11)$.
**Final answer:** $G = (-4, -11)$