What are the four quadrants in the Cartesian plane?

Q1 (first quadrant): x > 0, y > 0 — e.g., (3, 4). Q2: x 0 — e.g., (−2, 5). Q3: x 0, y < 0 — e.g., (4, −2). Points on the x-axis have y = 0; on the y-axis have x = 0; origin (0,0) is not in any quadrant.

What is the distance formula and how do you apply it?

Distance between two points P(x₁, y₁) and Q(x₂, y₂): d = √[(x₂−x₁)² + (y₂−y₁)²]. Steps: (1) Find x₂−x₁ and y₂−y₁, (2) Square both, (3) Add, (4) Take square root. Example: distance between (1, 2) and (4, 6) = √[(4−1)² + (6−2)²] = √[9+16] = √25 = 5.

How do you find the midpoint of a line segment?

Midpoint M of segment joining A(x₁, y₁) and B(x₂, y₂): M = ((x₁+x₂)/2, (y₁+y₂)/2). Simply take the average of the x-coordinates and average of y-coordinates. Example: midpoint of (2, 4) and (6, 8) = ((2+6)/2, (4+8)/2) = (4, 6).

Cartesian System

Coordinate Geometry • Class 9 Mathematics • NCERT • CBSE

The Cartesian coordinate system uses two perpendicular number lines (x-axis and y-axis) to locate points in a plane. Every point is represented as an ordered pair (x, y). The plane is divided into four quadrants by the two axes.

Key Formulas

Distance: d = √[(x₂−x₁)² + (y₂−y₁)²]
Distance from origin: d = √(x² + y²)
Midpoint: M = ((x₁+x₂)/2, (y₁+y₂)/2)
Section formula (m:n): P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))

Frequently Asked Questions

What are the four quadrants in the Cartesian plane?: Q1 (first quadrant): x > 0, y > 0 — e.g., (3, 4). Q2: x < 0, y > 0 — e.g., (−2, 5). Q3: x < 0, y < 0 — e.g., (−1, −3). Q4: x > 0, y < 0 — e.g., (4, −2). Points on the x-axis have y = 0; on the y-axis have x = 0; origin (0,0) is not in any quadrant.
What is the distance formula and how do you apply it?: Distance between two points P(x₁, y₁) and Q(x₂, y₂): d = √[(x₂−x₁)² + (y₂−y₁)²]. Steps: (1) Find x₂−x₁ and y₂−y₁, (2) Square both, (3) Add, (4) Take square root. Example: distance between (1, 2) and (4, 6) = √[(4−1)² + (6−2)²] = √[9+16] = √25 = 5.
How do you find the midpoint of a line segment?: Midpoint M of segment joining A(x₁, y₁) and B(x₂, y₂): M = ((x₁+x₂)/2, (y₁+y₂)/2). Simply take the average of the x-coordinates and average of y-coordinates. Example: midpoint of (2, 4) and (6, 8) = ((2+6)/2, (4+8)/2) = (4, 6).

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