Determine if the points (1,5),(2,3)and (_2,_11) …
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Sia ? 6 years, 6 months ago
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 that
AB + BC ≠ CA
BC + CA ≠ AB
and CA + AB ≠ BC
Hence, the given points are not collinear.
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