Question

The ratio in which the point (4,5) divides the line joining the points (2,3) and (7,8) is

• A. 6:7
• B. 5:4
• C. 4:3
• D. 2:3

Hint:

For internal division, use either x-coordinate or y-coordinate first, then verify with the other.

Answer 1

The Correct Option is D

Concept: Use the section formula. Let the point divide the line joining \[ A(2,3),\quad B(7,8) \] in the ratio \(m:n\).

Step 1: Apply section formula. For x-coordinate: \[ 4=\frac{7m+2n}{m+n} \] \[ 4m+4n=7m+2n \] \[ 2n=3m \] \[ m:n=2:3 \]

Step 2: Verify using y-coordinate. \[ 5=\frac{8m+3n}{m+n} \] Substituting \(m:n=2:3\), \[ 5=\frac{16+9}{5} =\frac{25}{5} =5 \] Verified. 2:3