VERY SIMPLE Coordinate Geometry

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SUMMARY

The discussion centers on determining whether the points A(5, -6), B(0, -1), and C(-4, 3) are collinear using the concept of equal slopes. Participants clarify that the slope between points A and B is -1, and the same applies to points B and C, indicating that they lie on the same line. The key takeaway is that equal slopes alone do not confirm collinearity unless the lines share a common point, which they do in this case. Thus, points A, B, and C are confirmed to be collinear.

PREREQUISITES
  • Understanding of coordinate geometry concepts
  • Knowledge of slope calculation using the formula (y2 - y1) / (x2 - x1)
  • Familiarity with the concept of collinearity
  • Basic graphing skills to visualize points and lines
NEXT STEPS
  • Study the properties of collinear points in coordinate geometry
  • Learn more about slope and its applications in geometry
  • Explore graphing techniques for visualizing points and lines
  • Review coordinate geometry textbooks or online resources for foundational concepts
USEFUL FOR

Students learning coordinate geometry, educators teaching mathematics, and anyone interested in understanding the principles of collinearity and slope calculations.

  • #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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