Equation of Perpendicular Line from Point to Segment

Consider the points A(4, 2), B(2, 5), and C(6, 7) in the coordinate plane.

You are to find the equation of the line that is perpendicular to line segment BC and passes through point A.

First, calculate the slope of the line segment BC:

Let the coordinates of B be (x₁, y₁) = (2, 5) and C be (x₂, y₂) = (6, 7).

The slope of line BC can be calculated using the formula:

$$ m_{BC} = \f\frac{y_{2} - y_{1}}{x_{2} - x_{1}} $$

Next, find the negative reciprocal of the slope of line BC, since the lines are perpendicular. Finally, use the point-slope form of the line equation to determine the equation of the line through point A(4, 2).