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 $(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$
x_1=0,x_2=-5,y_1=4,y_2=9
$= (- 2, 6)$
is the point
slope of AB is $\frac{9 - 4}{- 5} = - 1$
slope of line perpendicular to line AB is 1
equation of line perpendicular to line AB and passing through $(- 2, 6)$
is $(y - 6) = 1 (x + 2)$
$x - y + 8 = 0$

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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

ratio is 2:3 that m:nnow 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 pointslope of AB is 9−4−5=−1slope of line perpendicular to line AB is 1equation of line perpendicular to line AB and passing through (−2,6)is (y−6)=1(x+2)x−y+8=0

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 $2 : 3$