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 (x1, y1), (x2, y2) will be given by:

P (X,Y) = (\frac{m_1 \times_2 + m_2 \times_1}{m_1 + m_2}, \frac{m_1 Y_2 + m_2 Y_1}{m_1 + m_2})

here, point divides the line in ratio of m1 : m2

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) = (\frac{m (- 1) + n (5)}{m + n}, \frac{m (6) + n (3)}{m + n})

= (\frac{(- m + 5 n)}{m + n}, \frac{(6 m + 3 n)}{m + n})

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

\frac{(- m + 5 n)}{m + n} = 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: Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis.

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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