1 markMCQSection A

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

Q: 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

(a) x-axis — the midpoint is $(5.5, 0)$; since its y-coordinate is 0, it lies on the x-axis.

Q: What is the midpoint formula?

For points $(x_1,y_1)$ and $(x_2,y_2)$, the midpoint is $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.

Coordinate Geometry

Coordinate Geometry - Midpoint Formula

Options

(A)x-axis

(B)y-axis

(C)origin

(D)neither x-axis nor y-axis

Official Answer

(a) x-axis — the midpoint is $(5.5, 0)$ ; since its y-coordinate is 0, it lies on the x-axis.

midpoint formulacoordinate geometryx-axissection formulay-coordinate zero

Marking Scheme

11 mark: correct option (a) x-axis; full working credit: midpoint = $(5.5, 0)$ , and since y-coordinate = 0, it lies on the x-axis.

Hint

Apply the midpoint formula and check which coordinate becomes zero — if $y = 0$ , the point lies on the x-axis.

Quick Oral Answer

The midpoint of $(5,-4)$ and $(6,4)$ is $(5.5, 0)$ ; since its y-coordinate is zero, the point lies on the x-axis.

Analysis & Explanation

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.

Common Mistakes

1Confusing which axis corresponds to $y = 0$ versus $x = 0$ (mixing up x-axis and y-axis).
2Averaging the coordinates incorrectly, e.g., adding instead of dividing by 2.
3Assuming the point is the origin just because one coordinate is zero, without checking the other coordinate.

Interesting Facts

The midpoint formula is a direct special case ( $k=1$ ) of the section formula, which was systematically developed in coordinate geometry by René Descartes in the 17th century.

CBSE Class 10 sample papers regularly test the midpoint formula as a 1-mark MCQ because it combines arithmetic accuracy with conceptual understanding of axes.

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Frequently Asked Questions

What is the midpoint formula?

For points $(x_1,y_1)$ and $(x_2,y_2)$ , the midpoint is $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ .

How do you know if a point lies on the x-axis or y-axis?

A point lies on the x-axis if its y-coordinate is 0, and on the y-axis if its x-coordinate is 0.