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

Tests the midpoint formula and recognition of points lying on the coordinate axes.

Concept

• Midpoint of segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is $M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.
• A point lies on the x-axis exactly when its y-coordinate is 0.

Key points

• $M = \left(\frac{5+6}{2}, \frac{-4+4}{2}\right)$ = $(5.5, 0)$.
• Since $y = 0$ (and $x \ne 0$), the point lies on the x-axis — option (a).

Common mistakes

• Swapping which axis corresponds to $y = 0$ vs $x = 0$ ($y = 0$ is the x-axis, not the y-axis).
• Assuming $(5.5, 0)$ is the origin, which requires both coordinates to be 0.