JIPMAT 2024 (QA) - The points (2,2),(6,3) and (4,11) are vertices of : | PYQs + Solutions | AfterBoards
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JIPMAT 2024

Geometry
>
Triangles

Medium

The points (2,2),(6,3)(2,2),(6,3) and (4,11)(4,11) are vertices of :

Correct Option: 3
Let's identify the triangle with points (2,2), (6,3), and (4,11).
Side lengths using d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}:
AB = (6−2)2+(3−2)2\sqrt{(6-2)^2 + (3-2)^2} = 17\sqrt{17}\newlineBC = (4−6)2+(11−3)2\sqrt{(4-6)^2 + (11-3)^2} = 68\sqrt{68}\newlineAC = (4−2)2+(11−2)2\sqrt{(4-2)^2 + (11-2)^2} = 85\sqrt{85}
Checking for right angle using Pythagorean theorem:\newlineAC² = AB² + BC²\newline85=17+6885 = 17 + 68 ✓
Properties:\newline1. All sides different lengths: 17\sqrt{17} ≠ 68\sqrt{68} ≠ 85\sqrt{85} → Scalene\newline2. AC² = AB² + BC² → Right-angled at B
Therefore, this is both a right-angled and scalene triangle. NTA made an error. Marks were awarded for both the options 3 and 4.

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Given below are two statements:
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