**Q) Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis.**

**Ans: **

**Step 1: **By section formula, coordinates of point P (X, Y) which lies between two points (x_{1}, y_{1}), (x_{2}, y_{2}) will be given by:

P (X,Y) =

here, point divides the line in ratio of m_{1 :} m_{2 }

Now if the given points A (5, 3) and B(- 1, 6) are divided in the ratio of m : n, then:

coordinates of dividing point (x, y) =

=

Next, since this point lies on line Y axis, it means x = 0, this point will satisfy the equation

∴ = 0

∴ – m + 5 n = 0

∴ m = 5 n

∴ m : n = 5 : 1

**Therefore, the line segment divides the line in ratio of 5:1.**

**Check:** if we plot the given points and connect them:

*Here, we can see that Y axis is cutting them in a ratio where m is considerably larger than n. hence our answer is correct.*

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