Get To Know The Basic Geometry
What
Is A Cartesian Coordinate System?
- It is a coordinate system which specifies each point uniquely in a plane by a set of numerical coordinates.
- Which are the signed distances to the point from two fixed perpendicular oriented lines.
- Each reference line is called coordinate axis/axes.
- The two axes are : x axis and y axis
What Is Origin?
- Origin is the place where the two perpendicular axes intersect.
- The coordinate at the origin is (0,0)
- Let’s use
example below :
1. The format of
the coordinate should be (x , y)
2.
First
consider the x-axis and check out for the value
3.
Its -3
4.
So we write
it as (-3 , y)
5.
Now we will
consider the y-axis and check out for the value
6.
Its 2
7.
Now we have
found both x and y coordinates
8.
The
coordinate for the above point is (-3 , 2)
Gradient
- Gradient is
another word for ‘slope’.
- Higher the
gradient , steeper the slope
- To find the
gradient you just need only two points
· Assume we have the two points: 1. (X1 , Y1)
2. (X2, Y2)
- The standard
equation is to find gradient is
- In this situation :
- Consider the gradients of the following lines:
- A - has a positive gradient
- B - has a negative gradient
- C - no gradient
- D - infinite
gradient
Parallel And Perpendicular Lines
- If two lines
are parallel , they both have the same gradient
- In this
situation the gradient of both lines are 2
- If two lines
are perpendicular , products of their gradients equals to -1
- The equation
is as follows :
The Distance Between Two Points
- Assume the two points are : 1. (X1, Y1)
2. (X2, Y2)
- The equation is as follows:
- Pythagoras’s theorem is used
Midpoint Of A Line
- Assume the
two points are : 1. (X1, Y1)
2. (X2, Y2)
- The standard equation is as follows:
Building Up An Equation For A Straight Line
You just have to follow two steps
- . Find the gradient ( using the two given points)
- .Substitute the x and y coordinates to the equation and find the y – intercept (c)
- Special point: If a line passes via the origin the y –intercept equals to zero
