1. The problem states that the point $(4, 10)$ lies on the curve $y = f(x)$. This means when $x = 4$, $f(4) = 10$. 2. We need to find the coordinates of the corresponding point on the curve $y = 3f(x) - 2$. 3. Substitute $x = 4$ into the new curve equation: $$y = 3f(4) - 2$$ 4. Since $f(4) = 10$, substitute this value: $$y = 3 \times 10 - 2 = 30 - 2 = 28$$ 5. Therefore, the corresponding point on the curve $y = 3f(x) - 2$ when $x = 4$ is $(4, 28)$. Final answer: $(4, 28)$