Distance between two points, midpoint of two points, and finding gradient using two points
The Cartesian Plane isΒ β2βΒ dimensional surface, where positions represent coordinates of the formΒ β(x,y).Β The cartesian plane has
anΒ βxβ-axis: a horizontal line whereΒ βy=0β
aΒ βyβ-axis: a vertical line whereΒ βx=0.
the origin: where the two axes meet. BothΒ βxβΒ andΒ βyβΒ are zero here, so its coordinates areΒ β(0,0)β
The coordinatesΒ β(x,y)βΒ of a point tell you how far along theΒ βxβ-axis the point is, and how far along theΒ βyβ-axis the point is. By convention, positiveΒ βxβΒ coordinates are to the right of the origin, and positiveΒ βyβ-coordinates above the origin. Similarly, negativeΒ βxβΒ andΒ βyβΒ coordinates are to the left of and below the origin, respectively.
TheΒ βxβΒ andΒ βyβΒ axes divide the coordinate plane intoΒ β4βΒ regions called quadrants. They are often labeled with roman numeralsΒ βI,II,IIIβΒ andΒ βIV.Β
The distance between two pointsΒ β(x1β,y1β)βΒ andΒ β(x2β,y2β)βΒ is given by
The coordinates of the midpoint of two points is
The gradient of the line is a measure of its steepness. It is calculated by measuring the rise (change inΒ βyβ) in the line over a certain run (change inΒ βxβ).
The gradient of the line passing through the pointsΒ β(x1β,y1β)βΒ andΒ β(x2β,y2β)βΒ is
Nice work completing Distance, Midpoint, & Gradient, here's a quick recap of what we covered:
Exercises checked off
Distance between two points, midpoint of two points, and finding gradient using two points
The Cartesian Plane isΒ β2βΒ dimensional surface, where positions represent coordinates of the formΒ β(x,y).Β The cartesian plane has
anΒ βxβ-axis: a horizontal line whereΒ βy=0β
aΒ βyβ-axis: a vertical line whereΒ βx=0.
the origin: where the two axes meet. BothΒ βxβΒ andΒ βyβΒ are zero here, so its coordinates areΒ β(0,0)β
The coordinatesΒ β(x,y)βΒ of a point tell you how far along theΒ βxβ-axis the point is, and how far along theΒ βyβ-axis the point is. By convention, positiveΒ βxβΒ coordinates are to the right of the origin, and positiveΒ βyβ-coordinates above the origin. Similarly, negativeΒ βxβΒ andΒ βyβΒ coordinates are to the left of and below the origin, respectively.
TheΒ βxβΒ andΒ βyβΒ axes divide the coordinate plane intoΒ β4βΒ regions called quadrants. They are often labeled with roman numeralsΒ βI,II,IIIβΒ andΒ βIV.Β
The distance between two pointsΒ β(x1β,y1β)βΒ andΒ β(x2β,y2β)βΒ is given by
The coordinates of the midpoint of two points is
The gradient of the line is a measure of its steepness. It is calculated by measuring the rise (change inΒ βyβ) in the line over a certain run (change inΒ βxβ).
The gradient of the line passing through the pointsΒ β(x1β,y1β)βΒ andΒ β(x2β,y2β)βΒ is
Nice work completing Distance, Midpoint, & Gradient, here's a quick recap of what we covered:
Exercises checked off