1. The problem asks which of the given points lies inside the shaded triangular region in the fourth quadrant. 2. From the description, the shaded region is bounded above by a line from (-10, 10) to a point on the positive x-axis and below by the x-axis (y=0). 3. We need to find the equation of the line bounding the triangle above in the fourth quadrant. 4. The line passes through (-10, 10) and some point on the positive x-axis, say (a, 0). 5. The slope of the line is $$m = \frac{0 - 10}{a - (-10)} = \frac{-10}{a + 10}$$. 6. The line equation is $$y - 10 = m(x + 10)$$ or $$y = m(x + 10) + 10$$. 7. Since the shaded region is in the fourth quadrant, the x-intercept must be positive, so $$a > 0$$. 8. To find the exact line, we need the x-intercept. Since the problem does not provide it, we assume the line passes through the origin (0,0) for simplicity, which is a common boundary in such problems. 9. Check if the line through (-10, 10) and (0,0) fits: slope $$m = \frac{0 - 10}{0 - (-10)} = \frac{-10}{10} = -1$$. 10. Equation: $$y - 10 = -1(x + 10) \Rightarrow y = -x$$. 11. The shaded region is below this line and above the x-axis in the fourth quadrant. 12. For a point $(x,y)$ to be inside the shaded region: - $x > 0$ (fourth quadrant) - $0 \geq y \geq -x$ 13. Test each point: - (9, -7): $9 > 0$, $0 \geq -7 \geq -9$? Since $-7 \geq -9$ is true, inside. - (9, -10): $9 > 0$, $0 \geq -10 \geq -9$? $-10 \geq -9$ is false, outside. - (8, -9): $8 > 0$, $0 \geq -9 \geq -8$? $-9 \geq -8$ false, outside. - (8, -10): $8 > 0$, $0 \geq -10 \geq -8$? false, outside. - (7, -8): $7 > 0$, $0 \geq -8 \geq -7$? false, outside. 14. Only point (9, -7) lies inside the shaded region. **Final answer:** (9, -7)