Question

P is a point on the line segment joining the points \( (3, 2, -1) \) and \( (6, 2, -1) \).

• A. -1
• B. 1
• C. 2
• D. -2

Hint:

The midpoint formula is used to find the point that divides a line segment in a given ratio. Always ensure you apply the correct coordinates and divide the sums by 2.

Answer 1

The Correct Option is C

The formula for the point \( P \) on a line segment joining two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) is given by: \[ P = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \] Here, we are given the points \( (3, 2, -1) \) and \( (6, 2, -1) \). Using the formula, the coordinates of \( P \) are: \[ P = \left( \frac{3 + 6}{2}, \frac{2 + 2}{2}, \frac{-1 + (-1)}{2} \right) \] Simplifying: \[ P = \left( \frac{9}{2}, \frac{4}{2}, \frac{-2}{2} \right) \] \[ P = \left( 4.5, 2, -1 \right) \] Thus, the point \( P \) divides the line segment in the ratio 1:1 and is located at the point \( (4.5, 2, -1) \). Therefore, the correct value of \( P \) is \( \boxed{2} \).