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Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.?
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Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.?
Understanding Collinearity
Collinearity refers to the condition where three or more points lie on a single straight line. To determine if the points (1,5), (2,3), and (-2,-11) are collinear, we can use the concept of slopes.
Calculating Slopes
- Slope between (1,5) and (2,3)
The formula for slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
For points (1,5) and (2,3):
m1 = (3 - 5) / (2 - 1) = -2
- Slope between (2,3) and (-2,-11)
For points (2,3) and (-2,-11):
m2 = (-11 - 3) / (-2 - 2) = -14 / -4 = 3.5
- Slope between (1,5) and (-2,-11)
For points (1,5) and (-2,-11):
m3 = (-11 - 5) / (-2 - 1) = -16 / -3 ≈ 5.33
Analyzing the Slopes
- Conclusion
Since m1 (-2), m2 (3.5), and m3 (5.33) are not equal, the slopes between the pairs of points are different.
Final Verdict
- The points (1,5), (2,3), and (-2,-11) are not collinear because they do not share the same slope. Thus, they do not lie on a single straight line.
Collinearity refers to the condition where three or more points lie on a single straight line. To determine if the points (1,5), (2,3), and (-2,-11) are collinear, we can use the concept of slopes.
Calculating Slopes
- Slope between (1,5) and (2,3)
The formula for slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
For points (1,5) and (2,3):
m1 = (3 - 5) / (2 - 1) = -2
- Slope between (2,3) and (-2,-11)
For points (2,3) and (-2,-11):
m2 = (-11 - 3) / (-2 - 2) = -14 / -4 = 3.5
- Slope between (1,5) and (-2,-11)
For points (1,5) and (-2,-11):
m3 = (-11 - 5) / (-2 - 1) = -16 / -3 ≈ 5.33
Analyzing the Slopes
- Conclusion
Since m1 (-2), m2 (3.5), and m3 (5.33) are not equal, the slopes between the pairs of points are different.
Final Verdict
- The points (1,5), (2,3), and (-2,-11) are not collinear because they do not share the same slope. Thus, they do not lie on a single straight line.
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Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.?
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Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.?.
Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine if the points (1,5) ,(2,3) and (-2,-11) are collinear.?.
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