Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
The points $(1,2)$, $(3,6)$, and $(5,10)$ are:
The vertices of a right triangle
The vertices of an isosceles triangle
Collinear
Cannot be determined
Step-by-Step Solution
Key Concept: Use the distance formula: three points are collinear if the sum of the two smaller distances equals the largest distance.
$AB=\sqrt{4+16}=2\sqrt5$, $BC=\sqrt{4+16}=2\sqrt5$, $AC=\sqrt{16+64}=4\sqrt5$. [0.5 Mark]
Since $AB+BC=2\sqrt5+2\sqrt5=4\sqrt5=AC$, the three points are collinear. [0.5 Mark]
Correct Answer: Collinear
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