1. **State the problem:** Find the equation in point-slope form of the line perpendicular to the line passing through points (1, -1) and (4, 2), and passing through the point (2, 5). 2. **Find the slope of the given line:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$. Using points (1, -1) and (4, 2): $$m = \frac{2 - (-1)}{4 - 1} = \frac{3}{3} = 1$$. 3. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal. Since the original slope is $1$, the perpendicular slope is $$m_{\perp} = -\frac{1}{1} = -1$$. 4. **Use point-slope form:** The point-slope form is $$y - y_1 = m(x - x_1)$$. Using point (2, 5) and slope $-1$: $$y - 5 = -1(x - 2)$$. 5. **Match with given options:** The correct equation is: $$y - 5 = -(x - 2)$$. **Final answer:** $y - 5 = -(x - 2)$