SSC CHSL 2027: Coordinate Geometry Questions with Solved Examples

30/10/2026

SSC CHSL 2027: Coordinate Geometry Questions with Solved Examples

Coordinate Geometry is a mathematical topic that explains the position of points on a two-dimensional plane using numerical coordinates. It combines basic algebra and geometry to solve questions related to points, axes, distance and midpoint. Understanding these concepts can help candidates prepare for coordinate-based questions in competitive examinations.

For SSC CHSL 2027 preparation, candidates should understand the Cartesian coordinate system, four quadrants, coordinates of points and basic formulas. This guide covers important concepts, solved examples and practice questions.

1. What Is Coordinate Geometry?

Coordinate Geometry is a branch of mathematics in which the position of a point is represented using an ordered pair of numbers called coordinates.

A point is generally written as (x, y), where:

x-coordinate: Represents the horizontal position of the point.
y-coordinate: Represents the vertical position of the point.
Origin: The point where the X-axis and Y-axis intersect, represented by (0, 0).

For example, the point (3, 4) represents a position 3 units to the right and 4 units upward from the origin.

2. Understanding the Cartesian Coordinate Plane

The Cartesian coordinate plane consists of two perpendicular number lines:

X-axis: The horizontal number line.
Y-axis: The vertical number line.
Origin: The intersection point of both axes.

The two axes divide the plane into four regions called quadrants. Each quadrant has a specific combination of positive and negative coordinates.

Quadrant	X-coordinate	Y-coordinate	Sign
First Quadrant	Positive	Positive	(+, +)
Second Quadrant	Negative	Positive	(−, +)
Third Quadrant	Negative	Negative	(−, −)
Fourth Quadrant	Positive	Negative	(+, −)

Important: A point on the X-axis has a y-coordinate of zero, while a point on the Y-axis has an x-coordinate of zero. The origin is not part of any quadrant.

3. Important Types of Coordinates

Coordinates help identify the exact position of a point on the Cartesian plane.

Point	Position
(0, 0)	Origin
(5, 3)	First Quadrant
(−4, 6)	Second Quadrant
(−3, −5)	Third Quadrant
(7, −2)	Fourth Quadrant
(4, 0)	Positive X-axis
(0, −6)	Negative Y-axis

4. Important Coordinate Geometry Formulas

Learn the following basic formulas to solve numerical questions.

Concept	Formula
Distance between two points	√[(x₂ − x₁)² + (y₂ − y₁)²]
Midpoint	((x₁ + x₂)/2, (y₁ + y₂)/2)
Distance from origin	√(x² + y²)
Section on X-axis	y = 0
Section on Y-axis	x = 0

5. Solved Coordinate Geometry Questions for SSC CHSL 2027

Example 1: In which quadrant does the point (4, 5) lie?

Solution: Both coordinates are positive. Therefore, the point lies in the First Quadrant.

Example 2: Find the distance between the points (1, 2) and (4, 6).

Solution:

Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]

= √[(4 − 1)² + (6 − 2)²]

= √(9 + 16) = √25 = 5 units.

Example 3: Find the midpoint of the points (2, 4) and (6, 8).

Solution:

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

= ((2 + 6)/2, (4 + 8)/2)

= (4, 6).

Answer: (4, 6).

Example 4: Find the distance of the point (3, 4) from the origin.

Solution:

Distance = √(x² + y²)

= √(3² + 4²) = √(9 + 16)

= √25 = 5 units.

6. Common Mistakes to Avoid

Do not interchange the X-coordinate and Y-coordinate.
Remember that the X-coordinate is written first in an ordered pair.
Check the signs of both coordinates before identifying the quadrant.
Do not include points on the axes in any quadrant.
Apply the distance formula carefully and square both coordinate differences.
Remember to divide the sum of coordinates by 2 when finding the midpoint.

7. Practice Questions for SSC CHSL 2027

Q1. In which quadrant does the point (−5, 4) lie?

A) First Quadrant B) Second Quadrant C) Third Quadrant D) Fourth Quadrant

Answer: B) Second Quadrant

Q2. What are the coordinates of the origin?

A) (1, 1) B) (0, 1) C) (1, 0) D) (0, 0)

Answer: D) (0, 0)

Q3. Find the distance between (0, 0) and (6, 8).

A) 8 units B) 10 units C) 12 units D) 14 units

Answer: B) 10 units

Q4. Find the midpoint of the points (2, 6) and (4, 8).

A) (2, 4) B) (3, 7) C) (4, 6) D) (6, 8)

Answer: B) (3, 7)

Q5. A point has coordinates (7, −3). On which axis or quadrant does it lie?

A) First Quadrant B) Second Quadrant C) Third Quadrant D) Fourth Quadrant

Answer: D) Fourth Quadrant

8. Frequently Asked Questions

Q1. What is coordinate geometry?

Coordinate Geometry is the branch of mathematics that uses ordered pairs to represent points and study their positions on a plane.

Q2. What are the four quadrants in coordinate geometry?

The four quadrants are formed by the X-axis and Y-axis. Their coordinate signs are (+,+), (−,+), (−,−) and (+,−), respectively.

Q3. Which formulas are important in coordinate geometry?

The distance formula, midpoint formula and distance from the origin formula are useful basic formulas to understand and practise.

Conclusion

Coordinate Geometry introduces important concepts such as ordered pairs, quadrants, distance and midpoint calculations. For SSC CHSL 2027 preparation, candidates should understand the Cartesian coordinate system and practise basic numerical problems regularly. Learning these concepts can strengthen mathematical understanding and improve problem-solving skills.