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| 1. |
Determine if the points (1,5),(2,3)and (_2,_11) are collinear. |
| Answer» Let A {tex}\\rightarrow{/tex} (1, 5)B {tex}\\rightarrow{/tex} (2, 3)C {tex}\\rightarrow{/tex} (-2, -11)Then {tex}AB = \\sqrt {{{(2 - 1)}^2} + {{(3 - 5)}^2}} = \\sqrt {1 + 4} = \\sqrt 5{/tex}{tex}BC = \\sqrt {{{( - 2 - 2)}^2} + {{( - 11 - 3)}^2}}{/tex}{tex}= \\sqrt {{{( - 4)}^2} + {{( - 14)}^2}}{/tex}{tex}= \\sqrt {16 + 196} = \\sqrt {212}{/tex}{tex}CA = \\sqrt {{{[1 - (-2)]}^2} + [5 - {{( - 11)]}^2}}{/tex}{tex}= \\sqrt {{{(3)}^2} + {{(16)}^2}}{/tex}{tex}= \\sqrt {9 + 256} = \\sqrt {265}{/tex}We see thatAB + BC\xa0≠ CABC + CA ≠ ABand CA + AB ≠ BCHence, the given points are not collinear. | |