1. **State the problem:** Find the equation of the perpendicular bisector of the segment with endpoints A(-2, -2) and B(-10, 4). 2. **Find the midpoint of segment AB:** The midpoint formula is $$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$$. Calculate: $$\left(\frac{-2 + (-10)}{2}, \frac{-2 + 4}{2}\right) = \left(\frac{-12}{2}, \frac{2}{2}\right) = (-6, 1)$$. 3. **Find the slope of segment AB:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$. Calculate: $$m = \frac{4 - (-2)}{-10 - (-2)} = \frac{6}{-8} = -\frac{3}{4}$$. 4. **Find the slope of the perpendicular bisector:** The perpendicular slope is the negative reciprocal of the original slope. Calculate: $$m_{\perp} = -\frac{1}{m} = -\frac{1}{-\frac{3}{4}} = \frac{4}{3}$$. 5. **Write the equation of the perpendicular bisector:** Use point-slope form: $$y - y_1 = m_{\perp}(x - x_1)$$ where $(x_1, y_1)$ is the midpoint $(-6, 1)$. Calculate: $$y - 1 = \frac{4}{3}(x + 6)$$ 6. **Simplify the equation:** $$y - 1 = \frac{4}{3}x + \frac{4}{3} \times 6 = \frac{4}{3}x + 8$$ Add 1 to both sides: $$y = \frac{4}{3}x + 8 + 1 = \frac{4}{3}x + 9$$ **Final answer:** $$\boxed{y = \frac{4}{3}x + 9}$$