Question

If \( P \left( \frac{a}{2}, 4 \right) \) is the midpoint of the line segment joining the points \( A (-6, 5) \) and \( B (-2, 3) \), then the value of \( a \) is

• A. -8
• B. 3
• C. -4
• D. 4

Hint:

The midpoint of a line segment is the average of the x-coordinates and y-coordinates of the endpoints.

Answer 1

The Correct Option is C

Step 1: The midpoint formula is: \[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Step 2: Using the midpoint formula for the coordinates \( A (-6, 5) \) and \( B (-2, 3) \): \[ \left( \frac{-6 + (-2)}{2}, \frac{5 + 3}{2} \right) = \left( \frac{-8}{2}, \frac{8}{2} \right) = (-4, 4) \] Thus, \( a = -4 \).