Geometry - Coordinate Plane
- Coordinate Plane
- Coordinates
- Parts of the Coordinate Plane
- How to Plot Points on the Coordinate Plane
- How to Locate Points on the Coordinate Plane
- Fun Facts
- Practice Problems
- Frequently Asked Questions
Coordinate Plane
It is a two-dimensional plane formed by intersecting (crossing) two number lines. By intersecting these two lines we get a big plus sign which is called a coordinate plane.
Out of these two number lines, one should be horizontal and is known as the `x`-axis. The other should be vertical and is known as the `y`-axis.
These intersecting lines (`x`-axis and `y`-axis) are perpendicular and they intersect at a point called the origin (labeled as zero).
Let’s look at the below image to understand it more:
Coordinates
Coordinates are the points on the plane that indicate a particular position on the coordinate plane.
Typically, coordinates are denoted as `(x, y)`. Here, the `x`-coordinate is the perpendicular distance of the point from the y-axis along the `x`-axis. and, the `y`-coordinate is the perpendicular distance of the point from the `x`-axis along the `y`-axis.
For example: Let’s take `(2, 3)` as a point on the coordinate plane.
In this case, `2` corresponds to the value on the `x`-axis and `3` corresponds to the value on the `y`-axis.
Parts of the Coordinate Plane
1) Number lines:
- These are the lines that represent numbers or integers.
- When the two number lines intersect each other at `(0,0)`, they create a coordinate plane.
- We use them to locate/plot a specific position on the coordinate plane.
2) Origin:
- It is the intersecting point of the two number lines (horizontal and vertical).
- It is denoted by `O`.
- Here is the graphical representation of the origin on the coordinate plane:
3) Quadrants:
When two number lines intersect each other at the origin, they divide the coordinate plane into four equal parts; those parts are called quadrants.
Below is the coordinate representation of the four quadrants:
Let’s discuss them (four parts of quadrants) one by one.
Quadrant-Ⅰ: This quadrant contains only the positive values with respect to `x`-axis and `y`-axis respectively.
For example: `(2, 3)`
`(x, y)` or `(x>0, y>0)`
Quadrant-Ⅱ: It is the top left part of the quadratic plane. In this quadrant, `x` represents the negative value and `y` represents the positive value.
For example: `(-2, 3)`
`(-x, y)` or `(x<0, y>0)`
Quadrant-Ⅲ: It is the bottom left quadrant of the quadratic plane. In this quadrant `x`-axis and `y`-axis both contain negative values.
For example: `(-2, -3)`
`(-x, -y)` or `(x<0, y<0)`
Quadrant-Ⅳ: It is the bottom right quadrant of the quadratic plane. In this quadrant, the `x`-axis contains positive values and the `y`-axis contains negative values.
For example: `(2, -3)`
`(x, -y)` or `(x>0, y<0)`
How to Plot Points on the Coordinate Plane
To plot a point on the coordinate plane, we need to follow some steps-
- Step `1`: Start from the origin.
- Step `2`: To find the `x`-coordinate, move left/right from the origin.
- Step `3`: To find the `y`-coordinate move up/down from the `x`-point.
Example: Let’s plot `(``3``, ``4``)` on the coordinate plane.
- Step `1`: Look for the origin.
- Step `2`: Move `3` steps to the right from the origin.
- Step `3`: Now move, `4` steps upwards.
How to Locate Points on the Coordinate Plane
To locate any point on the coordinate plane follow these steps:
- Step `1`: First, observe the dot (point `P`) on the given graph.
- Step `2`: Check the quadrant of the dot.
- Step `3`: Observe, how many units this dot is far from the `x` and `y`-axis respectively.
Example: Let’s locate point `P` on the given graph.
We can observe a few points such as:
- `P` is in the first quadrant (Quadrant-Ⅰ).
- `P` is `2` units away from the origin in the positive direction(`x`-axis).
- `P` is `3` units away from the origin in the positive direction (`y`-axis).
Thus, based on the above points, we can conclude that the position of point `P` is `(2, 3)`.
Fun Facts
- On the coordinate points, the first number will always tell the value of the x-axis point and the second number will always tell the value of the `y`-axis point.
- Just by looking at the `(x, y)` coordinate you can tell the quadrant name.
- Point `x` will never move up/down on the coordinate; it only moves right/left.
- The value of `y` will never move left/right. It only moves upward/downwards on the coordinate plane.
Practice Problems
Q`1`: Given the coordinates `(−3, 5)`, in which quadrant does the point lie?
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
Answer: b
Q`2`: In which quadrant does the point `(7, -2)` lie?
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
Answer: d
Q`3`: Among the following points, which one lies in the third quadrant?
- (4, 2)
- (-3, 5)
- (-2, -7)
- (1, -3)
Answer: c
Q`4`: In which quadrant do both coordinates have positive values?
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
Answer: a
Q`5`. What are the coordinates of the point `A` on the given graph?
- (2,-4)
- (2,4)
- (-4,2)
- (4,2)
Answer: c
Frequently Asked Questions
Q`1`: What is the coordinate plane?
Answer: The coordinate plane is a two-dimensional system where points are located using ordered pairs of numbers `(x, y)`. It consists of two perpendicular number lines, the `x`-axis and `y`-axis, intersecting at the origin `(0, 0)`.
Q`2`: How do you determine in which quadrant a point lies?
Answer: A point's quadrant is determined by the signs of its `x` and `y` coordinates.
- If both are positive, the point is in Quadrant I.
- If `x` is negative and `y` is positive, it's in Quadrant II.
- If both are negative, it's in Quadrant III.
- If `x` is positive and `y` is negative, it's in Quadrant IV.
Q`3`: What is the significance of the origin in the coordinate plane?
Answer: The origin `(0, 0)` is the point where the `x`-axis and `y`-axis intersect. It serves as the reference point for all coordinates on the plane, and distances and directions are measured relative to the origin.