Topics
Distance, Midpoint, & Gradient
0 of 0 exercises completed
Distance between two points, midpoint of two points, and finding gradient using two points
Want a deeper conceptual understanding? Try our interactive lesson!
Cartesian Plane
2. Prior learning
The Cartesian Plane is 2 dimensional surface, where positions represent coordinates of the form (x,y). The cartesian plane has
an x-axis: a horizontal line where y=0
a y-axis: a vertical line where x=0.
the origin: where the two axes meet. Both x and y are zero here, so its coordinates are (0,0)
The coordinates (x,y) of a point tell you how far along the x-axis the point is, and how far along the y-axis the point is. By convention, positive x coordinates are to the right of the origin, and positive y-coordinates above the origin. Similarly, negative x and y coordinates are to the left of and below the origin, respectively.
Cartesian quadrants
2. Prior learning
The x and y axes divide the coordinate plane into 4 regions called quadrants. They are often labeled with roman numerals I,II,III and IV.
Distance between 2 points
2. Prior learning
The distance between two points (x1,y1) and (x2,y2) is given by
d=√(x1−x2)2+(y1−y2)2📖
Midpoint of 2 points
2. Prior learning
The coordinates of the midpoint of two points is
(2x1+x2,2y1+y2)📖
Slope as rise over run
SL Core 2.1
The gradient of the line is a measure of its steepness. It is calculated by measuring the rise (change in y) in the line over a certain run (change in x).
The gradient of the line passing through the points (x1,y1) and (x2,y2) is
m=x2−x1y2−y1📖
Nice work completing Distance, Midpoint, & Gradient, here's a quick recap of what we covered:
Skills covered
Exercises checked off
I'm Plex, here to help you understand this concept!