Math, asked by ronakjaiswal, 1 month ago

find the ratio in which the x axis divides the line segment joining the points (5, -6) and (-1, -4).also find the point of intersection with steps​

Answers

Answered by kamalhajare543
15

Answer:

Let the line segment A(5, -6) and B(-1, -4) is divided at point P(0, y) by y-axis in ratio m:n

\sf \implies \therefore \: x = \bold{ \frac{mx2+nx1}{m+n}} \\  \\ \sf \implies and \:  y = \frac{my2+ny1}{m+n} \\  \\  \sf \: Here, (x, y) = (0, y); (x1, y1) =\\ \sf (5, -6) and (x {}^{2} , y {}^{2} ) = (-1, -4) \\  \\ \sf \: So , \sf \implies \: 0 = \frac{m(-1)+n(5)}{m+n} \\  \\ \sf \implies 0 = -m + 5n \\  \\ \sf \implies \: m= 5n \\  \\ \sf \implies\frac{m}{n} \\  \\ \sf \implies= \frac{5}{1} \:  \\  \\  \sf\sf \implies \: \boxed{ \red{ \sf \: m:n = 5:1}}

Hence, the ratio is 5:1 and the division is internal.Now,

\sf \implies \: y = \frac{my2+ny1}{m+n} \\  \\ \sf \implies \: y = \frac{5(-4)+1(-6)}{5+1} \\  \\ \sf \implies y = \frac{-20-6}{6} \\  \\ \sf \implies \:  \bold{y = \frac{-26}{6}} \\  \\ \sf \implies  \bold{ \pink{y = \frac{-13}{3}}}

Hence,the coordinates of the point of division is

(0, -13/3)

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