VERY SIMPLE Coordinate Geometry

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The discussion revolves around determining if the points A(5, -6), B(0, -1), and C(-4, 3) are collinear using the concept of equal slopes. The correct method for calculating the slope between points is emphasized, with the slope of AB and BC both calculated as -1, indicating they share the same slope. Participants clarify that while equal slopes suggest parallel lines, the shared point B confirms that the lines AB and BC are collinear, meaning they lie on the same line. The importance of understanding basic coordinate geometry concepts is highlighted, as some participants struggle with the terminology and calculations involved. Overall, the conclusion is that the points are indeed collinear due to their equal slopes and shared point.
  • #31
Okay, I did as you said and...
A and B came back with -1
B and C came back with -1

I'm not sure what I am supposed to tell from that ... does "-1" on both mean that they are collinear?

no, it means that both are parallel but do you ever heard parallel lines intersecting at any point, therefore both lines AB and BC are not parallel but the same line and since points A, B and C lies on the same line they are collinear.

And "-1" doesn't mean that they are collinear. Any number will do well if you get it for both AB and BC.

Yes, "-1" on both means they have the same slope, and since they also share a point, they must be on the same line.

(incidentally, of course, if you check A and C, you should find the same )

I've said "No" and then just in very next post Tiny Tim has said "Yes", I think You are very confused. I want to clear it to you as well as Tiny Tim

Tiny Tim has said Yes for the current problem where you are getting a slope of "-1" but I've said No to tell you that every time in such problem you will not get "-1" as your answer. You don't have to care for that number "-1", only thing which you have to care is that whatever you get must be equal for both of the solution you have done.
To make it more clear assume that you have got "5" in place of "-1" but for both the solution then also it is right.
 

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