Question

The mid-point of the line segment joining the points (5, -4) and (6, 4) lies on :

• A. x-axis
• B. y-axis
• C. origin
• D. neither x-axis nor y-axis

Hint:

If two points have y-coordinates that are negatives of each other (like -4 and 4), their midpoint will always have a y-coordinate of 0 and thus lie on the x-axis.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The midpoint is the point exactly halfway between two endpoints. A point lies on the x-axis if its y-coordinate is 0, and on the y-axis if its x-coordinate is 0.
Step 2: Key Formula or Approach:
Midpoint formula: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
Step 3: Detailed Explanation:
1. Coordinates are \((x_1, y_1) = (5, -4)\) and \((x_2, y_2) = (6, 4)\). 2. Calculate the x-coordinate of the midpoint: \[ x = \frac{5 + 6}{2} = \frac{11}{2} = 5.5 \] 3. Calculate the y-coordinate of the midpoint: \[ y = \frac{-4 + 4}{2} = \frac{0}{2} = 0 \] 4. The midpoint is \((5.5, 0)\). Since the y-coordinate is 0, the point lies on the x-axis.
Step 4: Final Answer:
The midpoint lies on the x-axis.