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Answer: Yes, points are collinear.

Hints: First by using the values of vertices find determinant. If value of determinant is zero, then points are collinear.

$Given\! : \left ( 3,-2 \right ),\left ( 8,8 \right )\: and \: \left ( 5,2 \right )\! .$

$Explanation\! : V\! ertices\; are \left ( 3,-2 \right ),\left ( 8,8 \right )\: and \: \left ( 5,2 \right )\! .$

$Determinant\!= \begin{vmatrix} X_{1} &Y_{1} &1 \\ X_{2} &Y_{2} &1 \\ X_{3} &Y_{3} &1 \end{vmatrix}$

$= \begin{vmatrix} 3 &-2 &1 \\ 8 &8 &1 \\ 5 &2 &1 \end{vmatrix}$

$= 3\! \begin{vmatrix} 8 &1 \\ 2 &1 \end{vmatrix}-\left (-2 \right )\! \begin{vmatrix} 8 &1 \\ 5 &1 \end{vmatrix}+1\! \begin{vmatrix} 8 &8 \\ 5 &2 \end{vmatrix}$

$= 3\! \left (8-2 \right )+2\! \left ( 8-5 \right )+1\! \left ( 16-40 \right )$

$= 3\! \left ( 6 \right )+2\! \left ( 3 \right )+1\! \left ( -24 \right )$

$= 18+6-24$

$= 24-24$

$= 0$

Hence, points are collinear.

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