Determinants Are Used to Show That Three Points Lie on the Same

question 113

Multiple Choice

Determinants are used to show that three points lie on the same line (are collinear) . If
-The equation of a line passing through two distinct points (x1, y1) and (x2, y2) is given by $\left|\begin{array}{lll}x & y & 1 \\x_{2} & y 2 & 1 \\x_{3} & y_{3} & 1\end{array}\right|=0 . \text { Use the determinant to write an equation for the line passing through }(-6,9) \text { and }$
$( - 8,3 )$ . Express the line's equation in standard form.

• A) \(6 x - 2 y + 54 = 0\)
• B) \(9 x - 8 y - 18 = 0\)
• C) \(- 6 x + 2 y + 54 = 0\)
• D) \(3 x - 6 y - 72 = 0\)

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