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 formula is useful to find the average of two coordinates: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Answer 1

The Correct Option is C

The midpoint formula states:
\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Given points: \( A(-6,5) \) and \( B(-2,3) \),
\[ \left( \frac{-6 + (-2)}{2}, \frac{5 + 3}{2} \right) = \left( \frac{-8}{2}, \frac{8}{2} \right) = (-4,4) \] Comparing with \( P \left( \frac{a}{2}, 4 \right) \), we get:
\[ \frac{a}{2} = -4 \quad \Rightarrow \quad a = -4 \]