Final answer:
To find the coordinates of the point of congruency of the altitudes (H) in triangle ABC, we need to find the three altitudes of the triangle first. By finding the equations of the altitudes and solving a system of equations, we can determine the point of intersection which represents the point of congruency. The coordinates of H will represent the point where all three altitudes intersect and are congruent.
Step-by-step explanation:
To find the coordinates of the point of congruency of the altitudes (H) in triangle ABC, we need to find the three altitudes of the triangle first. The altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. We can use the formula for the equation of a line and the slope of the perpendicular line to find the equations of the altitudes. By solving the system of equations formed by the three altitudes, we can find the point of intersection, which is the point of congruency (H).
By solving the system of equations formed by the three altitudes, we can find the coordinates of the point of congruency (H). Substitute the equation of one altitude into the equations of the other two and solve for the coordinates of H. The coordinates of H will represent the point where all three altitudes intersect and are congruent.