Question

The coordinates of the mid-point of the line segment made by joining the points (-2, 6) and (-2, 10) are

• A. (-2, 8)
• B. (-2, 5)
• C. (-2, 3)
• D. (0, 2)

Hint:

Notice that the x-coordinates of both points are the same (-2). This means the line segment is vertical. For any vertical line, the x-coordinate of the midpoint will be the same as the endpoints' x-coordinate. You only need to find the average of the y-coordinates: (6+10)/2 = 8. This simplifies the problem.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question requires finding the coordinates of the midpoint of a line segment given the coordinates of its endpoints.
Step 2: Key Formula or Approach:
The coordinates of the midpoint of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) are given by the midpoint formula:
\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Step 3: Detailed Explanation:
The given endpoints are \( (-2, 6) \) and \( (-2, 10) \).
Let \( (x_1, y_1) = (-2, 6) \) and \( (x_2, y_2) = (-2, 10) \).
Calculate the x-coordinate of the midpoint:
\[ x_{mid} = \frac{x_1 + x_2}{2} = \frac{-2 + (-2)}{2} = \frac{-4}{2} = -2 \] Calculate the y-coordinate of the midpoint:
\[ y_{mid} = \frac{y_1 + y_2}{2} = \frac{6 + 10}{2} = \frac{16}{2} = 8 \] So, the coordinates of the midpoint are \( (-2, 8) \).
Step 4: Final Answer:
The coordinates of the mid-point are (-2, 8).