The coordinates of the orthocenter of the triangle whose sides are represented by the lines 4x - 7y + 10 = 0 , x + y = 5 and 7x + 4y = 15 are

Step-by-step solution

The given lines forming the triangle are 4x - 7y + 10 = 0 , x + y = 5 , and 7x + 4y = 15 . The slopes of the lines 4x - 7y + 10 = 0 and 7x + 4y = 15 are 4 7 and - 7 4 respectively. Since the product of their slopes is 4 7 (- 7 4 ) = -1 , these two lines are perpendicular to each other. The triangle formed by the given lines is a right-angled triangle. In a right-angled triangle, the orthocenter is the vertex where the right angle is formed. Thus, the orthocenter is the point of intersection of the perpendicular lin