# Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also, find the coordinates of the point of division. - Mathematics

Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also, find the coordinates of the point of division.

#### Solution

Suppose the x-axis divides the line segment joining the points A(3, −3) and B(−2, 7) in the ratio k : 1.
Using section formula, we get
Coordinates of the point of division = $\left( \frac{- 2k + 3}{k + 1}, \frac{7k - 3}{k + 1} \right)$

Since the point of division lies on the x-axis, so its y-coordinate is 0.

$\therefore \frac{7k - 3}{k + 1} = 0$

$\Rightarrow 7k - 3 = 0$

$\Rightarrow k = \frac{3}{7}$

So, the required ratio is $\frac{3}{7}$  : 1 or 3 : 7.

Putting k = $\frac{3}{7}$ , we get

Coordinates of the point of division = $\left( \frac{- 2 \times \frac{3}{7} + 3}{\frac{3}{7} + 1}, 0 \right) = \left( \frac{- 6 + 21}{3 + 7}, 0 \right) = \left( \frac{15}{10}, 0 \right) = \left( \frac{3}{2}, 0 \right)$

Thus, the coordinates of the point of division are  $\left( \frac{3}{2}, 0 \right)$ .

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Chapter 6: Co-Ordinate Geometry - Exercise 6.3 [Page 29]

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Exercise 6.3 | Q 19 | Page 29

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