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Find the ratio in which the point P(x, 2) divides the line segment joining the points A $(12,5)$ and B $(4,-3)$. Also, find the value of x.
Find the ratio in which the point P(x, 2) divides the line segment joining the points A $(12,5)$ and B $(4,-3)$. Also, find the value of x.
CBSE | Class 10 | Co-ordinate Geometry | Exercise 14.3 | Maths | RD Sharma
Find the ratio in which the point P(x, 2) divides the line segment joining the points A $(12,5)$ and B $(4,-3)$. Also, find the value of x.

Let’s P divide the line joining A and B and let it divide the segment in the ratio k:$1$

Now, by using the section formula for the y – coordinate we have

$2=(-3k+5)/(k+1)$

$2(k+1)=-3k+5$

$2k+2=-3k+5$

$5k=3$

$k=3/5$

so, P divides the line segment AB in the ratio of $3:5$

By Using the value of k, we get the x – coordinate as

$x=12+60/8=72/8=9$

Hence, the coordinates of point P is $(9,2)$

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