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 the y-coordinates of two points are equal in magnitude but opposite in sign (like $-4$ and $4$), their average is always 0.
This immediately implies that the midpoint will have $y = 0$, which places it directly on the x-axis, saving you calculation time!

Answer 1

The Correct Option is A

Step 1: Recall what it means to lie on the x-axis.
A point lies on the x-axis exactly when its y-coordinate is 0, so we only really need to track the y-coordinates of the two given points.
Step 2: Look at just the y-coordinates first.
The given points are $(5,-4)$ and $(6,4)$; their y-values, $-4$ and $4$, are exact opposites, so averaging them gives $\frac{-4+4}{2}=0$ before we even touch the x-coordinates.
Step 3: Confirm with the full midpoint.
Averaging the x-coordinates too gives $\frac{5+6}{2}=5.5$, so the midpoint is $(5.5,0)$, which has y-coordinate 0 and therefore lies on the x-axis.
\[ \boxed{\text{x-axis}} \]