Notes: Coordinate Geometry – “The Line”
Key things to know for this chapter
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The Coordinate Plane – How to draw a coordinate plane. X and Y axis labelled, points spaced
out equally on axis
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How to read and write coordinates on a plane (X value 1st, Y value 2nd)
•
How to use formulas to find the following pieces of information
Midpoint
Slope
Distance
Equation of a line
•
Verify if a line is parallel or perpendicular to another line
•
How to verify a point is on a line
•
Use simultaneous equations to find the point of intersection of two lines
The Coordinate plane is a 2 dimensional plane that consists of two axes, the X axis and the Y axis.
Where both axes meet in the centre is called the origin ( 0, 0) and numbers get either more
positive or more negative the further away from the origin you go along the axes
We can use the coordinate plane to describe the location of something by giving two measurements,
an X coordinate (How far left or right it is on the horizontal axis) and a Y coordinate (How far up or
down it is on the vertical axis)
For example: The black dot in the coordinate plane above is located at the point (3,4)
We give coordinates in the format ( X , Y ) where the x measurement goes first, and the Y
measurement second. So, that means this point is located 3 boxes to the right on the x axis, and 4
boxes up on the Y axis. A handy way to remember which comes first is to remember that X comes
before Y in the alphabet!
Midpoint Formula
When given two coordinates on a plane, we can use the midpoint formula to find the location of the
halfway point between those two coordinates on a straight line. You can see by looking at the
formula, that your answer will give you a coordinate ( x, y) and we can get that coordinate by finding
half of the X value (x1 +x2 / 2) and half of the Y value (y1 +y2 / 2)
Take the two points ( -4, 5 ) and (2 , -3) for example. To find the midpoint between these two points,
we can substitute them in to our midpoint formula. Our two x values are -4 and 2, and our two Y
values are 5 and -3 substituting them in to our formula we get ( -4+2 / 2 , 5 -3 /2) or (-2/2, 2/2)
Thus giving us a midpoint of (-1,1)
Slope Formula
Slope refers to the gradient or ‘steepness’ of a line. It is represented by the
rate of change in the Y axis and the X axis
Slopes can be positive (trends up from left to right) or negative (trends down
from left to right) or have no slope at all (zero slope/Horizontal line)
The slope can be found between two points by finding the change
in y values divided by the change in x values.
which is often referred to as rise over run
Distance Formula
To use distance formula, label your points (x1, y1) and (x2, y2) and substitute them in to the formula!
Parallel and Perpendicular Lines