If $$P4$$,−$$1$$,$$3$$,$$Q0$$,$$6$$,$$7$$,R−$$2$$,$$1$$,$$9$$ are vertices of a triangle PQR,the equation of the median through R is x−$$im=y$$−$$cs=z$$−ty, then $$m+y+s+t+i+c$$ $$=$$ $$_____$$ .(where$$[.] denotes greatest integer $$function) and m,s,y are numerically least possible integers.

Question

If  $$P4$$,−$$1$$,$$3$$,$$Q0$$,$$6$$,$$7$$,R−$$2$$,$$1$$,$$9$$ are vertices of a triangle PQR,the equation of the median through R is  x−$$im=y$$−$$cs=z$$−ty, then $$m+y+s+t+i+c$$ $$=$$  $$_____$$ .(where$$[.] denotes greatest integer $$function) and m,s,y are numerically least possible integers.

Infinity Learn · Accepted Answer

Midpoint of the side  PQ is  $$S=4+02$$,−$$1+62$$,$$3+72=2$$,$$52$$,$$5The$$ direction ratios of the median  $$RSare2+2$$,$$52$$−$$1$$,$$5$$−$$9=4$$,$$32$$,−$$4=8$$,$$3$$,−$$8Hence$$, the equation of the median is x−$$28=y$$−$$523=z$$−$$5$$−$$8Therefore$$,   $$m+y+s+t+i+c$$ $$=$$ $$2+52+5+8+3$$−$$8=12.5=12$$

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If P4,−1,3,Q0,6,7,R−2,1,9 are vertices of a triangle PQR,the equation of the median through R is x−im=y−cs=z−ty, then m+y+s+t+i+c = _____ .(where[.] denotes greatest integer function) and m,s,y are numerically least possible integers.

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