Question 81 markMCQSection A

  1. The mid-point of the line segment joining the points (5,−4)(5, -4) and (6,4)(6, 4) lies on : (a) x-axis (b) y-axis (c) origin (d) neither x-axis nor y-axis

Coordinate Geometry
Mid-point formula

Options

(A)x-axis
(B)y-axis
(C)origin
(D)neither x-axis nor y-axis

Official answer

(a) x-axis — mid-point = (5.5,0)(5.5, 0); since y=0y = 0 and x≠0x \ne 0, the point lies on the x-axis.

Answer keywords:mid-point formulacoordinate geometryx-axisy-coordinate zero(11/2, 0)average of coordinates

Marking scheme

  1. 1.1 mark: correct option (a) x-axis.
  2. 2.Justification (internal): mid-point = (112,0)\left(\frac{11}{2}, 0\right); y-coordinate 0 with x≠0x \ne 0 ⇒ point on x-axis.

Hint

Average the coordinates; if the resulting y-coordinate is 00 (and x≠0x \ne 0), the point lies on the x-axis.

Quick oral answer

The mid-point is 5.5 comma 0; since its y-coordinate is zero but x is non-zero, the point lies on the x-axis.

Common mistakes

  1. 1.Confusing the conditions: thinking y=0y = 0 means the point is on the y-axis (it is actually the x-axis).
  2. 2.Choosing 'origin' because one coordinate is 0, forgetting the origin needs BOTH coordinates to be 0.
  3. 3.Subtracting instead of adding coordinates in the formula, e.g. computing (6−5)/2(6-5)/2 or (4−(−4))/2(4-(-4))/2 and misreading the result.

Analysis and explanation

The mid-point of (5,−4)(5, -4) and (6,4)(6, 4) comes out to (5.5,0)(5.5, 0), and any point with y-coordinate 0 (and x ≠ 0) lies on the x-axis.


Concept

  • Mid-point formula: (x1+x22,y1+y22)\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 steps

  • Mid-point = (5+62,−4+42)=(5.5,0)\left(\frac{5+6}{2}, \frac{-4+4}{2}\right) = (5.5, 0).
  • y=0y = 0 and x=5.5≠0x = 5.5 \ne 0 → point lies on the x-axis, option (a).

Common mistakes

  • Option (b): confuses the condition — y-axis needs x = 0, but here x≠0x \ne 0.
  • Option (c): origin needs BOTH coordinates zero; here only y is zero.
  • Missing the quick symmetry that −4 and +4 are equal and opposite, so they cancel to give y = 0 instantly.

Real-world

  • Recognising that mirror-image y-values (−4 and +4) always average to zero is a fast exam trick worth spotting on sight.

Interesting facts

The mid-point formula is a special case of the section formula with ratio 1:1 — dividing a segment into two equal parts.

René Descartes, who founded coordinate geometry in the 17th century, reportedly conceived the idea of locating points by coordinates while watching a fly move across his ceiling.

Question details

Q8 of 53 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Basic)
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Coordinate Geometry
Topic
Mid-point formula
Bloom's level
apply
Syllabus topic
Unit 3: Coordinate Geometry — Section and Mid-point Formula
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

How do I decide if a point lies on the x-axis or y-axis?

A point lies on the x-axis when its y-coordinate is 0, and on the y-axis when its x-coordinate is 0. If both are 0, it is the origin.

Why does the y-coordinate become 0 here?

The two y-values are −4 and +4, which are equal and opposite. Their sum is 0, so their average (−4+4)/2(-4+4)/2 is also 0, placing the mid-point on the x-axis.

Is (112,0)\left(\frac{11}{2}, 0\right) the same as the origin?

No. The origin is (0,0)(0, 0). Here x=11/2=5.5x = 11/2 = 5.5 is not zero, so the point is on the x-axis but well away from the origin.