VERY SIMPLE Coordinate Geometry

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Homework Help Overview

The discussion revolves around determining whether the points A(5, -6), B(0, -1), and C(-4, 3) are collinear using the concept of equal slopes in coordinate geometry.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss calculating the slope between points A and B, and then between B and C, to check for collinearity. There are questions about the correctness of slope calculations and the implications of equal slopes.

Discussion Status

Several participants have provided guidance on calculating slopes and have pointed out the importance of using consistent methods. There is an ongoing exploration of the relationship between equal slopes and collinearity, with some participants questioning the understanding of basic concepts in coordinate geometry.

Contextual Notes

Some participants express concerns about the original poster's understanding of coordinate geometry concepts, suggesting a need for further study. There are references to the potential confusion surrounding the definitions of points and slopes.

  • #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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