Find the coordinates of C that divides the segment AB in ratio AC/CB=-3/2 ,where A(1,-2) and B(7,4).Find also equation of straight line pass thru C(perpendicular to AB)?

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Answer 1 · 2015-10-03T02:26:54

#C(23/5,8/5)#
#5x+5y-31=0#

#m=3, n=2#
#A(1,-2) => x_1=1, y_1=-2#
#B(7,4) => x_2=7, y_2=4#

#C(x,y)=?#

#x=(n*x_1+m*x_2)/(m+n) = (2*1+3*7)/(2+3)=23/5#

#y=(n*y_1+m*y_2)/(m+n) = (2*(-2)+3*4)/(2+3)=8/5#

#C(23/5,8/5)#

#k_(AB)=(y_2-y_1)/(x_2-x_1)=(4-(-2))/(7-1)=6/6=1#

#k*k_(AB)=-1 => k=-1/(k_(AB))=-1/1=-1#

#y=kx+n#
#y=-x+n#

#C in y =>8/5=-23/5+n => n=8/5+23/5=31/5#

#y=-x+31/5#

#5x+5y-31=0#