Question

The ratio in which y- axis divides the line joining the points (5, -2) and (-2, 3) is​

Answer 1

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Step-by-step explanation:

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Answer 2

$\Large{\sf{Given }}$

• Two points are (5,-2) and (-2,3) .

• Y - axis divides line joining these two points.

$\Large{\sf{To\: Find}}$

• The ratio in which y axis divide the line joining the given two points .

$\Large{\sf{Solution }}$

Firstly let's see the internal division formula .

If we have 2 points namely P(x1,y1) and Q ( x2,y2) and a point R(x,y) divides the line PQ in ratio m : n then the formula we will use internal division formula .

$\boxed{\sf{Formula = x \implies \frac{[m. x_2 ] + [ n. x_1 ] }{ m+n } , y \implies \frac{[ m . y_2] + [ n.y_1] }{ m+n} }}$

Let's assume that y axis will divide the line in k:1. Where P( 5,-2) and Q(-2,3) .

Using the above mentioned formula .

Where $\sf{x_1 = 5 \:,\: x_2 = -2 }$

and $\sf{y_1 = -2 \:,\: y_2 = 3}$

Coordinates of dividing point will ( 0, y)

$\sf{\implies 0 = \frac{[ k . ( -2) ] + [ 1 . ( 5)] }{k+1} }$

$\sf{\implies 0 ( k+1) = -2k + 5 }$

$\sf{\implies 0 + 2k = 5 }$

$\sf{\implies \frac{k}{1} = \frac{5}{2} }$

$\underline{\sf{\purple{ k : 1 = 5 : 2 }}}$

So y axis will divide the line PQ in 5 : 2.