A rectangle has two opposite vertices at the points (1, 2) and (5, 5). If the other vertices lie on the line x = 3, then the coordinates of the other vertices are

Let A ≡ (1, 2) and C ≡ (5, 5). Since the vertices B and D lie on the line x = 3, therefore, let B ≡ (3, y1) and D ≡ (3, y2).Since AC and BD bisect each other, so they have same middle pointi.e,  y1+y22=2+52 or  y1+y2=7                                 (1)Also, BD2 = AC2⇒ (y1 – y2)2 = (1 – 5)2 + (2 – 5)2 = 25or y1 – y2 = ± 5                                   (2)Solving (1) and (2), we get y1 = 6, y2 = 1 or y1 = 1, y2 = 6Thus, the other vertices of the rectangle are (3, 1)and (3, 6).