Question

The ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and  (3, -5, 8)  is  2 : m.  
The value of m is:

• A. 2
• B. 3
• C. 4
• D. 1

Hint:

When using the section formula, set the x-coordinate of the point to the value given by the plane (in this case, \( x = 0 \)) and solve for the unknown ratio.

Answer 1

The Correct Option is B

The coordinates of the two points are given as: \[ P_1(-2, 4, 7) \quad {and} \quad P_2(3, -5, 8). \] The YZ-plane is represented by \( x = 0 \), meaning the x-coordinate of the point dividing the line segment must be 0. Let the point dividing the line segment in the ratio \( 2 : m \) be \( P(x, y, z) \). Using the section formula for the x-coordinate, we have: \[ x = \frac{m \cdot x_1 + 2 \cdot x_2}{m + 2}. \] Substituting the values of \( x_1 = -2 \) and \( x_2 = 3 \), we get: \[ 0 = \frac{m \cdot (-2) + 2 \cdot 3}{m + 2}. \] Simplifying: \[ 0 = \frac{-2m + 6}{m + 2}. \] For the numerator to be zero, we solve: \[ -2m + 6 = 0 \quad \Rightarrow \quad m = 3. \] Thus, the value of \( m \) is 3.