Question

The coordinates of the point which divides the line segment joining the points \((4, -3)\) and \((8, 5)\) in the ratio 3:1 internally is:

• A. (3, 7)
• B. (7, 3)
• C. (-7, -3)
• D. (-3, -7)

Hint:

Use the section formula to find a point dividing a line segment in a given ratio.

Answer 1

The Correct Option is A

To find the coordinates of the point dividing the line segment in the ratio \(m:n\), we use the section formula: \[ x = \frac{m x_2 + n x_1}{m + n}, \quad y = \frac{m y_2 + n y_1}{m + n} \] Here, \(m = 3\), \(n = 1\), \(x_1 = 4\), \(y_1 = -3\), \(x_2 = 8\), and \(y_2 = 5\). Substituting these values: \[ x = \frac{3 \times 8 + 1 \times 4}{3 + 1} = \frac{24 + 4}{4} = \frac{28}{4} = 7 \] \[ y = \frac{3 \times 5 + 1 \times (-3)}{3 + 1} = \frac{15 - 3}{4} = \frac{12}{4} = 3 \] Thus, the coordinates are \( (7, 3) \). Therefore, the correct answer is option (2).