Question

In what ratio is the line segment joining the points (-2,-3) and (3,7) divided by the y axis . Also find the coordinates of points of division .

Answer 1

the ratio is 2 isto 3 and coordinates are 0 and 1

Answer 2

The ratio in which the line segment the points (-2,-3) and (3,7) divided by the y axis is 2:3 and the coordinates of the point of division is P(0,1)

Explanation:

The given points are A(-2,-3) and B(3,7). Let the ratio in which the line segment is dived is k:1. Let the required point is (0,y). Using section formula as :

$P(0,y)=[\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}]\\\\P(0,y)=[\dfrac{k(3)+1(-2)}{k+1},\dfrac{k(7)+1(-3)}{k+1}] \\\\P(0,y)=[\dfrac{3k-2}{k+1},\dfrac{7k-3}{k+1}]$

On equating,

$\dfrac{3k-2}{k+1}=0\\\\k=\dfrac{2}{3}$

The ratio in which the line segment the points (-2,-3) and (3,7) divided by the y axis is 2:3.

Now,

$y=\dfrac{7k-3}{k+1}=\dfrac{7(2/3)-3}{(2/3)+1}\\\\y=1$

The coordinates of the point of division is P(0,1)

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