Question

Find the coordinates of the point which divides the line segment joining \((2, -3)\) and \((7, 9)\) in the ratio \(3:2\).

• A. (5, 4.2)
• B. (5, 8.2)
• C. (4, 10.2)
• D. (3, 12.2)

Hint:

To find the point dividing a segment in ratio \(m:n\), always clarify the order of division and use the formula accordingly.

Answer 1

The Correct Option is A

To solve the problem, we need to find the coordinates of the point dividing the line segment joining $(2, -3)$ and $(7, 9)$ in the ratio $3 : 2$.

1. Understanding the Section Formula: 
If a point $P$ divides the line segment joining points $A(x_1, y_1)$ and $B(x_2, y_2)$ in the ratio $m : n$, then the coordinates of $P$ are given by:

$ P = \left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\right) $

2. Substituting the Given Values:
Here,
$ x_1 = 2, \quad y_1 = -3 $
$ x_2 = 7, \quad y_2 = 9 $
$ m = 3, \quad n = 2 $

3. Calculating the $x$-coordinate:
$ x = \frac{3 \times 7 + 2 \times 2}{3 + 2} = \frac{21 + 4}{5} = \frac{25}{5} = 5 $

4. Calculating the $y$-coordinate:
$ y = \frac{3 \times 9 + 2 \times (-3)}{3 + 2} = \frac{27 - 6}{5} = \frac{21}{5} = 4.2 $

5. Final Coordinates:
The point dividing the line segment is $ \boxed{(5, 4.2)} $.