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Question

Find equation of the perpendicular to segment joining the point A(0,4) and B(5,9) and passing through the point P divide segment AB in the ratio 2:3

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Solution

ratio is 2:3 that m:n
now point that divides AB is (mx2+nx1m+n,my2+ny1m+n)
x_1=0,x_2=-5,y_1=4,y_2=9
=(2,6)
is the point
slope of AB is 945=1
slope of line perpendicular to line AB is 1
equation of line perpendicular to line AB and passing through (2,6)
is (y6)=1(x+2)
xy+8=0

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