Question

The co-ordinates of the mid-point of the line segment joining the points (4, -4) and (-4, 4) are

• A. (4, 4)
• B. (0, 0)
• C. (0, -4)
• D. (-4, 0)

Hint:

The midpoint (0,0) is also known as the origin. If you notice that the coordinates of the two points are opposites of each other (like (a, -b) and (-a, b)), their midpoint will always be the origin.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The midpoint of a line segment is the point that lies exactly halfway between the two endpoints. Its coordinates are the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Step 2: Key Formula or Approach:
The formula for the midpoint \((x_m, y_m)\) of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ (x_m, y_m) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]

Step 3: Detailed Explanation:
The given endpoints are \((4, -4)\) and \((-4, 4)\).
Let \((x_1, y_1) = (4, -4)\) and \((x_2, y_2) = (-4, 4)\).
Calculate the x-coordinate of the midpoint:
\[ x_m = \frac{4 + (-4)}{2} = \frac{0}{2} = 0 \] Calculate the y-coordinate of the midpoint:
\[ y_m = \frac{-4 + 4}{2} = \frac{0}{2} = 0 \] So, the coordinates of the midpoint are \((0, 0)\).

Step 4: Final Answer:
The co-ordinates of the mid-point are (0, 0).