Find Value of k to Make 3 Points Collinear

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Discussion Overview

The discussion revolves around finding the value of k that would make the points (3,9), (7,k), and (-1,6) collinear. Participants explore different methods to approach the problem, including the use of the distance formula and slope calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants suggest using the distance formula to determine collinearity, while others question its relevance to the problem.
  • One participant defines collinearity as the condition where three points lie on the same straight line and proposes two methods: finding the line equation or using slope calculations.
  • A participant mentions using a linear regression utility to derive a function and suggests that k equals 12 based on the output.
  • Another participant critiques the use of a linear regression utility for this specific problem, implying that simpler methods should suffice.

Areas of Agreement / Disagreement

Participants express differing opinions on the appropriate methods to solve the problem, with no consensus on the best approach or the value of k.

Contextual Notes

There is uncertainty regarding the relevance of the distance formula and the appropriateness of using linear regression for this problem. The discussion does not resolve the mathematical steps needed to find k.

Who May Find This Useful

Students or individuals interested in geometry, algebra, or problem-solving techniques related to collinearity and linear equations.

cheab14
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The question reads: find the value of k to make the points (3,9) (7, k), and (-1,6) collinear.

Does this involve using the distance formula? Whether or not it does, how would I go about solving this problem?
 
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cheab14 said:
The question reads: find the value of k to make the points (3,9) (7, k), and (-1,6) collinear.

Does this involve using the distance formula? Whether or not it does, how would I go about solving this problem?

What does collinear mean? That means that those 3 points lie on the same straight line.
So there are two methods you can use to find k.

You can find the straight line equation through all the points and then sub the co-ord you want to get.

OR you can use what you know about the slope of a line to aid you in an easier fashion.
 
ok thank u!
 
question 2

write an equation for the line that contains (0, 3) and is perpendicular to the line 6x-2y=1.

So for this question, I've found the slope of the line 6x-2y=1 which was 3. But would the slope for line (0, 3) be -1/3?
 
Yes.
 
Last edited by a moderator:
Oh, dear! A "linear regression" utility to determine the equation of a line through 2 points. Do you use a calculator to add 1+ 1?

You're just "showin' off" aren't you dexteronline?
 
I could be done easier
 

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