$M$ and $N$ are two points on the X-axis and Y-axis respectively.
$P (3, 2)$ divides the line segment $M N$ in the ratio $2 : 3$ .
Find the coordinates of $M$ and $N$ .

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Solution

Let the coordinates of M and N be $(x .0)$ and $(0, y)$
Refer image,
$P (3, 2) = P (\frac{2 \times 0 + 3 x}{2 + 3}, \frac{2 y + 3 \times 0}{2 + 3}$
$= P (\frac{3 x}{5}, \frac{2 y}{5})$
$3 = \frac{3 x}{5} \Rightarrow x = 5 a n d 2 = \frac{2 y}{5} \Rightarrow y = 5$
Thus, the coordinates of M and N are $M (5, 0)$ and $N (0, 5)$

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M and N are two points on the X-axis and Y-axis respectively.P(3,2) divides the line segment MN in the ratio 2:3.Find the coordinates of M and N.

Let the coordinates of M and N be (x.0) and (0,y)Refer image,P(3,2)=P(2×0+3x2+3,2y+3×02+3=P(3x5,2y5)3=3x5⇒x=5and2=2y5⇒y=5Thus, the coordinates of M and N are M(5,0) and N(0,5)

$M$ and $N$ are two points on the X-axis and Y-axis respectively.
$P (3, 2)$ divides the line segment $M N$ in the ratio $2 : 3$ .
Find the coordinates of $M$ and $N$ .