Collinearity using area
Three points are collinear if they lie on one straight line.
Practice This ConceptMain explanation
Teacher explanation
The easiest coordinate test for collinearity is the area method. If the area of the triangle formed by the three points is zero, then the points do not make a triangle at all; they lie on the same line. This is a fast and dependable exam check.
Example
The points (1, 1), (3, 3), and (5, 5) have zero area, so they are collinear.
Simple analogy
Zero area means one straight line.
Common confusion
Students may rely only on a rough graph or slope idea and miss a calculation error.
Exam tip
If the area becomes zero, stop and write collinear. Do not continue to search for triangle properties.
Answer writing and exam use
1-mark use
Write the exact meaning of collinearity using area in one clean line.
2-mark use
Define collinearity using area and add one example or condition.
3-mark use
Explain collinearity using area, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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