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Section Formula

Find the rati...

Question

Find the ratio in which the point P (-1, y) lying on the line segment joining A (-3, 10) and B (6,-8) divides it. Also , find the value of y.

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Solution

Point dividing a line in the ratio 1:m formed by joining $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .
x = $fraction numerator m x subscript 1 plus x subscript 2 over denominator 1 plus m end fraction$ y = $fraction numerator m y subscript 1 plus y subscript 2 over denominator 1 plus m end fraction$

Let us assume that point P (-1,y) divided the line joining A(-3,10) and B(6,-8) in the ratio 1:m
Then
$negative 1 equals fraction numerator negative 3 m plus 6 over denominator 1 plus m end fraction minus 1 minus m equals negative 3 m plus 6 2 m equals 7 m equals 7 over 2$

Hence P divides the line in the ratio of 2:7

$y space equals space fraction numerator 10 m minus 8 over denominator 1 plus m end fraction equals fraction numerator 10 left parenthesis begin display style 7 over 2 end style right parenthesis minus 8 over denominator 1 plus begin display style 7 over 2 end style end fraction equals fraction numerator 27 over denominator begin display style bevelled 9 over 2 end style end fraction equals 6$
y = 6

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Similar questions

Q. Find the ratio in which the line segment joining the points

(- 3, 10)

(6, - 8)

is divided by x-axis and y-axis respectively. Also find the coordinates of points of division.

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