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Question

The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is _______.


  1. equilateral

  2. isosceles

  3. scalene

  4. right angled


Solution

The correct option is B

isosceles


Distance between two points P(x1,y1) and Q(x2,y2) is given by:
Distance = (x2x1)2+(y2y1)2 

Using distance formula, find the length of all the three sides with vertices A(0, 6), B(-5, 3), C(3, 1).
AB2=(50)2+(36)2        =(52+32)=34BC2=(3(5))2+(13)2        ={(8)2+22}=68AC2=(16)2+(30)2        =(3)2+(5)2=34
AB2=AC2
 AB=AC.
Hence, ΔABC is isosceles.

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