1. **Problem statement:** Describe the transformation that maps triangle P onto triangle Q. 2. **Observing the graph:** Triangle P has vertices approximately at $(-2,1)$, $(-1,3)$, and $(-1,1)$. Triangle Q has vertices approximately at $(6,7)$, $(7,5)$, and $(6,3)$. 3. **Identify the center of enlargement:** The dotted lines connecting corresponding vertices converge near the point $(1,2)$, so the center of enlargement is $(1,2)$. 4. **Calculate the scale factor:** - Take a vertex of P, for example $(-2,1)$, and its corresponding vertex in Q, $(6,7)$. - Calculate the distance from the center to each vertex: $$d_P = \sqrt{(-2 - 1)^2 + (1 - 2)^2} = \sqrt{(-3)^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$$ $$d_Q = \sqrt{(6 - 1)^2 + (7 - 2)^2} = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50}$$ 5. **Find the scale factor $k$:** $$k = \frac{d_Q}{d_P} = \frac{\sqrt{50}}{\sqrt{10}} = \sqrt{\frac{50}{10}} = \sqrt{5} \approx 2.236$$ 6. **Final description:** Enlargement with a scale factor of $\sqrt{5}$ and centre $(1,2)$.