newin

Sure, if you provide specific coordinates for the vertices of a triangle, I can help you find the orthocenter. The orthocenter is the point where the altitudes of the triangle intersect, and using the method you've outlined, we can calculate its coordinates step-by-step for your specific triangle. Please provide the coordinates of the vertices \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), and I'll assist you with the calculations. Finding the coordinates of the orthocenter of a triangle involves determining the intersection point of the altitudes of the triangle. The altitudes are the perpendicular lines drawn from each vertex to the opposite side. Given the vertices of a triangle \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), here's a step-by-step method to find the orthocenter: 1. **Find the slopes of the sides:** - Slope of \( BC \): \( m_{BC} = \frac{y_3 - y_2}{x_3 - x_2} \) - Slope of \( AC \): \( m_{AC} = \frac{y_3 - y_1}{x_3 - x_...