Question

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Answer 1

Correct Question :-

Find the ratio in which the line joining(-2,5) and (-5,-6) is divided by the line y = - 3. Hence find the point of intersection.

Solution :-

line joining (-2,5) and (-5,-6) is divided by the line y = - 3

The general form of coordinates of points on line y = - 3 is (x, - 3)

Let the coordinates of points which divides be P(x, - 3)

By using section formula

$P(x,y) = \bigg( \dfrac{mx_2 + nx_1 }{m + n} , \dfrac{my_2 + ny_1 }{m + n} \bigg)$

(-2,5) (-5,-6)

Here

• x1 = - 2
• y1 = 5
• x2 = - 5
• y2 = - 6

$\implies P(x, - 3) = \bigg( \dfrac{m( - 5) + n( - 2) }{m + n} , \dfrac{m( - 6)+ n(5) }{m + n} \bigg)$

$\implies P(x , - 3)= \bigg( \dfrac{ - 5 m - 2n }{m + n} ,\dfrac{- 6m+ 5n}{m + n} \bigg)$

Equating Y-coordinates

$\implies - 3 = \dfrac{- 6m+ 5n}{m + n}$

$\implies - 3(m + n) = - 6m+ 5n$

$\implies - 3m - 3n = - 6m+ 5n$

$\implies - 3m + 6m=5n + 3n$

$\implies 3m = 8n$

$\implies \dfrac{m}{n} = \dfrac{8}{3}$

$\implies m :n = 8:3$

Therefore the the line segment is divided in the ratio of 8 : 3.

Now, equating x coordinates

$\implies x = \dfrac{ - 5 m - 2n }{m + n}$

m : n = 8 : 3 , So m = 8, n = 3

$\implies x = \dfrac{ - 5(8) - 2(3) }{8+ 3}$

$\implies x = \dfrac{ - 40 - 6 }{11}$

$\implies x = \dfrac{ - 46}{11} = - 4.182$

Hence the point of intersection is (-4.182, - 3)