Question

Find the co-ordinates of point P where P is the midpoint of a line segment AB with A($-4$, 2) and B(6, 2). 

Hint:

The midpoint of a line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Answer 1

Let $A(-4, 2) = (x_1, y_1)$ and $B(6, 2) = (x_2, y_2)$, and let $P(x, y)$ be the midpoint of AB.
Step 1: According to the midpoint theorem,
\[ x = \frac{x_1 + x_2}{2}, \quad y = \frac{y_1 + y_2}{2} \]
Step 2: Substitute the given values.
\[ x = \frac{-4 + 6}{2} = \frac{2}{2} = 1 \]
\[ y = \frac{2 + 2}{2} = \frac{4}{2} = 2 \]
Step 3: Write the coordinates of midpoint P.
\[ P(x, y) = (1, 2) \]
Step 4: Conclusion.
Therefore, the co-ordinates of midpoint $P$ are (1, 2).
Correct Answer: $P(1, 2)$