Question

Show that the points A (6,4), B(9,7) and C(11, 9) are collinear

Answer 1

Step-by-step explanation:

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Answer 2

$Let \: A(6,4) = ( x_{1} , y_{1} ) , \\B(9,7) = ( x_{2} , y_{2} ) , \:and \\</p><p>C(11,9) = ( x_{3} , y_{3} ) , are \: vertices \:of \: a \\triangle$

$\underline { \blue { By \: using \:Area \:of \:the \: triangle :}}$

$Area \: of \:the \: \triangle$

$=\frac{1}{2}| x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) +x_{3}(y_{1}-y_{2}) |$

$= \frac{1}{2}| 6(7-9)+9(9-4)+11(4-7)|\\= \frac{1}{2}| 6(-2)+9(5)+11(-3)|\\= \frac{1}{2}| -12+45-33| \\= \frac{1}{2}| 45 - 45| \\= \frac{1}{2} \times 0 \\= 0$

$\pink {Area \: of \:the \: \triangle = 0}$

Therefore.,

$\green {Hence, A, B \:and \: C \:points \: are \: collinear }$

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