The orthocenter of the triangle whose sides are given by 4x−7y+10=0, x+y−5=0, 7x+4y−15=0 .

4x−7y+10=0 …………………(1) x+y−5=0 ……………………….(2)7x+4y−15=0 …………………(3)(1), (3) are perpendicular lines, hence point of intersection of (1) (3) is the orthocenter.Solving (1), (3)Orthocenter=(1,  2)