Determine if the points $(1, 5), (2, 3)$ and $(-2, -11)$ are collinear using the distance formula.
Step-by-Step Solution
Key Concept: $AB = \sqrt{(2-1)^2 + (3-5)^2} = \sqrt{1 + 4} = \sqrt{5}$. $BC = \sqrt{(-2-2)^2 + (-11-3)^2} = \sqrt{16 + 196} = \sqrt{212} = 2\sqrt{53}$. $AC = \sqrt{(-2-1)^2 + (-11-5)^2} = \sqrt{9 + 256} = \sqrt{265}$. Since $AB + BC <br>eq AC$, not collinear.
$AB = \sqrt{5}$, $BC = \sqrt{212} = 2\sqrt{53}$, $AC = \sqrt{265}$. [1.0 Mark]
Since $AB + BC
eq AC$, the points are NOT collinear. [1.0 Mark]
---
🎯 Official CBSE Marking Scheme:
Calculating distances $AB, BC, AC$: 1.0 Mark
Testing collinearity condition $AB + BC = AC$: 1.0 Mark
Correct Answer: