In which quadrant is the point (–4, –3) located? A. I B. II C. III D. IV
C
Understanding Quadrants in the Coordinate Plane
The coordinate plane, also known as the Cartesian plane, is formed by two perpendicular number lines: the horizontal x-axis and the vertical y-axis. They intersect at a point called the origin (0, 0).
These two axes divide the plane into four regions called quadrants. The quadrants are numbered counterclockwise, starting from the upper right region.
- Quadrant I: This is the upper right region. Points in this quadrant have a positive x-coordinate and a positive y-coordinate. (x > 0, y > 0)
- Quadrant II: This is the upper left region. Points in this quadrant have a negative x-coordinate and a positive y-coordinate. (x < 0, y > 0)
- Quadrant III: This is the lower left region. Points in this quadrant have a negative x-coordinate and a negative y-coordinate. (x < 0, y < 0)
- Quadrant IV: This is the lower right region. Points in this quadrant have a positive x-coordinate and a negative y-coordinate. (x > 0, y < 0)
| Quadrant | x-coordinate sign | y-coordinate sign | Point example |
|---|---|---|---|
| I | + | + | (2, 5) |
| II | – | + | (–2, 5) |
| III | – | – | (–2, –5) |
| IV | + | – | (2, –5) |
Locating the Point (–4, –3)
We are given the point with coordinates $\left(x, y\right) = \left(–4, –3\right)$.
Let's analyze the signs of its coordinates:
- The x-coordinate is –4, which is a negative value (x < 0).
- The y-coordinate is –3, which is also a negative value (y < 0).
We need to find the quadrant where both the x-coordinate and the y-coordinate are negative.
Determining the Quadrant for (–4, –3)
Comparing the signs of the coordinates of the point (–4, –3) with the signs in each quadrant:
- Quadrant I: (+, +) – Does not match (x is –, y is –).
- Quadrant II: (–, +) – Does not match (y is –).
- Quadrant III: (–, –) – Matches (x is –, y is –).
- Quadrant IV: (+, –) – Does not match (x is –).
Since both the x-coordinate (–4) and the y-coordinate (–3) are negative, the point (–4, –3) is located in the Quadrant III.
Revision Table: Coordinate Plane Quadrants
| Concept | Description |
|---|---|
| Coordinate Plane | Formed by x and y axes intersecting at the origin. |
| Quadrants | Four regions of the coordinate plane defined by the axes. |
| Point (–4, –3) | Has a negative x-coordinate (–4) and a negative y-coordinate (–3). |
| Quadrant III | The region where both x and y coordinates are negative. |
Additional Information: Points on Axes
Points that lie on the axes are not considered to be in any quadrant.
- Points on the x-axis have a y-coordinate of 0 (e.g., (5, 0), (–5, 0)).
- Points on the y-axis have an x-coordinate of 0 (e.g., (0, 5), (0, –5)).
- The origin (0, 0) is where the axes intersect.
Understanding the signs of coordinates in each quadrant is fundamental for plotting points and solving geometry problems on the coordinate plane.
Important Questions from Co-ordinate Geometry
The area of a quadrilateral whose vertices are (3,0), (4,5), (-1,4) and (-2,-1) taken in order, is:
The coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4) is:
The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
The ratio between the radius of the base and the height of a cylinder is 3:4. If its volume is 38,808 cm³, then using \( \pi = \frac{22}{7} \), find the diameter of the cylinder.
In ΔABC if ∠A = 50° and ∠B = 70°, find the measure of exterior angle A.
