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STD 11 - rectangular cartensian co-ordinates — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - rectangular cartensian co-ordinates1 Mark
MCQ
A triangle with vertices $(4, 0),\, (-1, -1),\, (3, 5)$ is
  • ✓
    Isosceles and right angled
  • B
    Isosceles but not right angled
  • C
    Right angled but not isosceles
  • D
    Neither right angled nor isosceles
✓

Answer

Correct option: A.
Isosceles and right angled
a
(a) Let $A\,(4,\,\,0),\,\,B\,( - 1,\, - 1),\,\,C\,(3,\,\,5)$ then $AB = \sqrt {26} ,$ $AC = \sqrt {26} $ and $BC = \sqrt {52} \,\,i.e.,\,\,\,AB = AC$.

Hence triangle is isosceles. Also, ${(BC)^2} = A{B^2} + A{C^2}$

Hence triangle is right angled also.

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