Use a Determinant to Determine Whether the Points (-5,1), (-8,-1)and $$\left| \begin{array} { c c c } - 5 & 1 & 1 \\- 8 & - 1 & 1 \\1 & 5 & 1\end{array} \right| = 0 \text {; therefore, the points are collinear. }$$

question 49

Multiple Choice

Use a determinant to determine whether the points (-5,1) , (-8,-1) and (1,5) are collinear. ?

• A) \[\left| \begin{array} { c c c }
• - 5 & 1 & 1 \\
• - 8 & - 1 & 1 \\
• 1 & 5 & 1
• \end{array} \right| = 0 \text {; therefore, the points are collinear. }\]
• B) \[\left| \begin{array} { c c c }
• - 5 & 1 & 1 \\
• - 8 & - 1 & 1 \\
• 1 & 5 & 1
• \end{array} \right| = 1 \text {; therefore, the points are not collinear }\]

---

Definitions:

Longitudinal Study

A research design that involves repeated observations of the same variables (e.g., people) over short or long periods of time.

Factor Analysis

A statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.

Gene Variations

Differences in the sequences of DNA among individuals, which contribute to the genetic diversity within species.

Educational Achievement

The accomplishment of educational milestones or the attainment of knowledge or skills, often measured through grades, diplomas, or standardized test scores.