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Question

The area of an equilateral triangle with the equation of base as x+y-2=0 and the opposite vertex with the coordinates (2, -1) is  sq. units.
  1. 13
  2. 123
  3. 23
  4. 133


Solution

The correct option is B 123
Let 'p' be the length of the altitude i.e. the perpendicular distance from the point (2, -1) on the line x+y-2=0.
p=(21212+12=12Also, we know that altitude of anequilateral triangle with side a is 3a2(Area = 12×p×a=3a24)3a2=12a=23Area=3a24=34×23=123sq. units

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