Question

Find the ratio in which the y-axis divides the line segment joining the
points (6, - 4) and (-2, – 7). Also find the point of intersection.​

Answer 1

Given ,

the y axis divides the line segment joining the points (6, -4) and (-2, -7)

Let , the y axis divides the given line segment in the ratio m : n

We know that , the section formula is given by

$\boxed{ \tt{x = \frac{m x_{2} + n x_{1}}{m + n} \: \: \: \: \:y= \frac{m y_{2} + ny_{1}}{m + n}}}$

And the coordinate of y axis = (0 , y)

Thus ,

$\tt \implies 0 = \frac{ -2 m + 6n}{ m + n}$

$\tt \implies0 = - 2m + 6n$

$\tt \implies2m = 6n$

$\tt \implies \frac{m}{n} = \frac{6}{2}$

$\tt \implies \frac{m}{n} = \frac{3}{1}$

Therefore , the ratio in which y axis divides the given line segment is 3 : 1

Now ,

$\tt \implies y = \frac{3( - 7) +1( - 4) }{3 + 1}$

$\tt \implies y = \frac{ - 21 - 4}{4}$

$\tt \implies y = - \frac{25}{4}$

Therefore , the coordinate of point of intersection is (0 , -25/4)

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