Question

The quadrant in which the point divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally lies, is

• A. 1st quadrant
• B. 2nd quadrant
• C. 3rd quadrant
• D. 4th quadrant

Answer 1

The Correct Option is D

The given points are \( P(7, -6) \) and \( Q(3, 4) \), and the point divides the line segment joining these points in the ratio 1:2 internally.
The formula to find the coordinates of a point dividing the line segment in the ratio \( m:n \) is:
\[ x = \frac{m \cdot x_2 + n \cdot x_1}{m + n}, \quad y = \frac{m \cdot y_2 + n \cdot y_1}{m + n} \] Substitute the values: \[ x = \frac{1 \cdot 3 + 2 \cdot 7}{1 + 2} = \frac{3 + 14}{3} = \frac{17}{3} \approx 5.67 \] \[ y = \frac{1 \cdot 4 + 2 \cdot (-6)}{1 + 2} = \frac{4 - 12}{3} = \frac{-8}{3} \approx -2.67 \] The coordinates of the dividing point are approximately \( (5.67, -2.67) \). This point lies in the 4th quadrant.

Therefore, the correct answer is (D): 4^th quadrant