\( \left. \begin{array} { l l } { C \notin [ A B ] } & { C \in A B } \end{array} \right. \quad A ( 3,4 ) , B ( 8 , - 1 ) \)
Upstudy AI Solution
Answer
Solution
Answered by UpStudy AI and reviewed by a Professional Tutor
![](/pmw/light_bulb.png?etag=525fd69ac661e11754e2fc9f1b18a4ee)
![](/pmw/spiral_notepad.png?etag=abe3906b7558c543a7b30ba53a3b5a5b)
Extra Insights
In this scenario, we're dealing with points \( A(3, 4) \) and \( B(8, -1) \). The notation \( C \notin [AB] \) suggests that point C is not on the line segment connecting points A and B, while \( C \in AB \) implies C is actually an option on the extended line that includes the points A and B. To check that, we can find the equation of the line and see if C lies on that line or outside segment AB. This serves as a visual and analytical interpretation for understanding relative positions in geometry! To visualize it, you can plot the points on a Cartesian grid! Draw a line connecting A and B then check if your imaginary point C falls between A and B on this line. If C has coordinates that satisfy the line equation between these two points but is outside the endpoints, it’s in line but not on the segment. Alternatively, if C falls directly between them on the connecting line, it’s part of the segment themselves! Navigating through point positions is fundamental in geometry and can often reveal interesting relationships!