Class 9 Mathematics Chapter 3 Coordinate Geometry

Key Concept: Street Plan

c) 3${rd}$ North-South and 6${th}$ East-West

[Solution Description]

Coordinates in street plans follow $(North-South street, East-West street)$. First value (3) indicates the 3${rd}$ North-South street. Second value (6) indicates the 6${th}$ East-West street. Their intersection identifies the location.

Key Concept: Cartesian System Basics

a) Horizontal and Vertical axes

[Solution Description]

According to the syllabus summary point 2-3, the horizontal line is called $x$-axis and vertical line is $y$-axis. These two form the basis of coordinate axes in the Cartesian system.

Key Concept: Quadrant Sign Convention

b) Quadrant II

[Solution Description]

Key Concept: Coordinates of Origin

c) $(0,0)$

[Solution Description]

The origin is the point where both $x$-axis and $y$-axis intersect. As per syllabus point 9, its coordinates are always $(0,0)$ because it has zero distance from both axes.

Key Concept: Number of References Needed

c) To determine position uniquely in two-dimensional space

[Solution Description]

On a number line, only one reference is needed. But in a plane, positions exist in two dimensions (left-right and up-down). Two perpendicular references like $x$-axis and $y$-axis are required to uniquely identify any position through their intersection point.

Key Concept: Horizontal Line Identification

a) $x$-axis

$x$-axis

Key Concept: Points on Axes

a) $(4, 0)$

[Solution Description] Points on the x-axis have their y-coordinate as $0$. Among the options, only $(4, 0)$ has y-coordinate $0$, making it lie on the x-axis.

Key Concept: Cartesian Plane Components

d) Origin

[Solution Description] The $x$-axis (horizontal) and $y$-axis (vertical) cross each other at a specific point. According to the syllabus, this intersection is called the origin. All coordinates are measured relative to this point, which has the coordinates $(0,0)$.

Key Concept: Quadrants Division

c) Four

[Solution Description]

The coordinate axes consist of perpendicular x-axis and y-axis intersecting at origin. These divide the plane into four equal parts called quadrants.

Key Concept: Point on Axis

b) y-axis

[Solution Description]

A point with coordinates $(0, y)$ lies on the $y$-axis since its $x$-coordinate is 0. Here, the $x$-coordinate is 0 and $y$-coordinate is $-5$, so it lies on the $y$-axis.

Key Concept: Coordinates Order

a) $(2, 5)$

[Solution Description]

The abscissa ($x$-coordinate) is the perpendicular distance from the $y$-axis (2 units). The ordinate ($y$-coordinate) is the perpendicular distance from the $x$-axis (5 units). Thus, coordinates = $(2, 5)$.