# Number Plane and Cartesian Geometry

### Theory, Formulae and Practice

#### Welcome to Sydney Based Aussie Math Tutor NSW, your go-to destination for expert private math tutoring online. On this page you will learn the basic of graph in a clear easy way. The page is made by our experienced tutors in Sydney for the students in Sydney. Thus, master concepts such plotting the points, quadrants and plotting a line equation in this lesson.

## CARTESIAN PLANE

**A Number Plane** is a flat-surfaced two-dimensional grid that extends infinitely and is formed by the intersection of two number lines. One number line runs horizontally and is called **the X-axis**. The other number line runs vertically and is called **the Y-axis**. These lines intersect at a point called the origin and is denoted as (0,0).

**Quadrants:** The four sections of the Cartesian plane divided by the x-axis and y-axis. The X-axis and the Y-axis divides the Number plane into four sections called as the Quadrants. The x and the y values of any point maybe positive or negative depending on which quadrant it lies.

##### The image below shows the number plane along with the Quadrants

### The Co-ordinates of a point on a Number Plane

**The Co-ordinates of any point **is determined by its distance from the X-axis and the Y-axis. The x co-ordinate is the distance of the point away from the Y-axis and the y co-ordinate is the distance of the point away from the X-axis.

##### To find these distances, we draw a segment perpendicular to the X-axis and the Y-axis as they are the Shortest Distance to the Axes.

##### The image below shows how to find x and y co-ordinates of a give point.

### Exercise: Practice Questions on Plotting the Points

**Question : Plot the following points on a graph:**

**a)** ( 0, 3 ) **b)** ( 1, 2 ) **c)** ( 2, 1 )

**d)** ( 3, -4 ) **e)** ( -4, -4 ) **f)** ( -5, 3 )

### Answers

###### WhatsApp us at +61-0422 768 717

## Love what you're learning? Level up with Aussie Math Tutor NSW. Join now!

### Equation of a Line

##### The most common form of the equation of a line is called as the **slope-intercept form**: **y = mx + c**

**Where: **

**(x,y) are the co-ordinates of a point on the graph**

**m is the slope of the line. **The slope represents the steepness of the line.

**c is the constant. **The constant represents the distance away from the centre O (0,0).

##### The formula for the slope of a line is given by:

### Distance and Midpoint

### Relationship Between Slope and Parallel or Perpendicular Lines

**Parallel Lines**

**Definition:**Two lines are parallel if they have the same slope and never intersect.**Slope Relationship:**##### If two lines are parallel, their slopes are equal.

##### If line 1 has a slope m1 and line 2 has a slope m2, then for the lines to be parallel: m1=m2

**Perpendicular Lines**

**Definition:**Two lines are perpendicular if they intersect at a right angle (90 degrees).**Slope Relationship:**##### If two lines are perpendicular, the product of their slopes is −1

##### If line 1 has a slope m1 and line 2 has a slope m2, then for the lines to be perpendicular:

**m1×m2=−1**