QQuestionMathematics
QuestionMathematics
Give an example from your classroom of three collinear points.
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Step 1:I'll solve this problem by providing an example of three collinear points with a clear, step-by-step explanation:
Step 2:: Understanding Collinearity
Collinear points are points that lie on the same straight line. To demonstrate this, I'll choose a simple coordinate system example.
Step 3:: Selecting Collinear Points
- Point C: $$(2, 3)
Let's choose three points that clearly lie on the same line:
Step 4:: Verifying Collinearity
\frac{3 - 2}{2 - 0} = \frac{1}{2}
To confirm these points are collinear, we can use the slope method. If the slopes between any two points are the same, the points are collinear. Slope between A and B: Slope between B and C:
Step 5:: Confirming the Result
Since both slopes are $$\frac{1}{2}$$, these points lie on the same line $$y = \frac{1}{2}x + 2$$.
Final Answer
The points (- 2, 1), (0, 2), and (2, 3) are collinear, forming a straight line with the equation y = \frac{1}{2}x + 2.
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