Question

The mid-point of the line segment joining the points \( A (-2, 8) \) and \( B (-6, -4) \) is:

• A. \( (-6, -4) \)
• B. \( (-4, 2) \)
• C. \( (2, 6) \)
• D. \( (-4, -6) \)

Hint:

The mid-point of a line segment is the average of the x-coordinates and the average of the y-coordinates of the two points.

Answer 1

The Correct Option is B

The mid-point \( M \) of a line segment joining two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by the formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right). \] Substitute \( A (-2, 8) \) and \( B (-6, -4) \): \[ M = \left( \frac{-2 + (-6)}{2}, \frac{8 + (-4)}{2} \right) = \left( \frac{-8}{2}, \frac{4}{2} \right) = (-4, 2). \] Thus, the correct answer is \( \boxed{(-4, 2)} \).