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Question

The equation of the base of an equilateral triangle is X +Y =2 and vertex is (2, -1) length of its side is :

A
(12)
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B
(32)
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C
(23)
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D
2
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Solution

The correct option is C (23)
GivenP(x1,y1)=(2,1)isthevetexofanequilateraltriangle.Theequationofitsbaseisx+y=2x+y2=0.Tofindoutthesideofthegivenequilateraltriangle=?SolutionThepependiculardistaceofthevertexfromthebaseofatriangleisitsheight.Foranequilateraltriangleofsidea,theheighth=32aa=2h3.Nowweapplytheformulap=ax1+by1+ca2+b2whenP(x1,y1)isthepointandax+by+c=0istheequationoftheline.HereP(x1,y1)=(2,1),a=1,b=1&c=2.p=h=∣ ∣1×2+1×(1)+(2)12+12∣ ∣units=12units.Thesidea=2h3=2×123units=23units.

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