Saved Bookmarks
| 1. |
Show that the points (4, 2,), (7, 5) and (9, 7) do not form a triangle |
|
Answer» Answer: Step-by-step EXPLANATION: Let A(4, 2), B(7,5) and C(9,7) be the given points......... By using Distance formula, AB = √[(7-4)2 + (5-2)2] => √[(3)2 + (3)2] => √(9 + 9) =>√18 => 3√2........... BC = √[(9-7)2 + (7-5)2] => √[(2)2 + (2)2] => √(4 + 4) => √8 => 2√2......... AC = √[(9-4)2 + (7-2)2] => √[(5)2 + (5)2] => √(25 + 25) => √50 => 5√2....... 3√2 + 2√2 = 5√2 AB + BC = AC. If any three points form a triangle, the sum of any two sides MUST be greater than the third side.... But here they are collinear points....... So, they dont form a triangle. Hence, proved! |
|