Coaching Centre
The Cartesian plane
Plotting and reading points on the Cartesian plane in all four quadrants, the origin, axes and ordered pairs (x, y).
Axes and coordinates
The Cartesian plane has a horizontal $x$-axis and a vertical $y$-axis crossing at the origin $(0, 0)$. A point is described by an ordered pair $(x, y)$: go across $x$ first, then up or down $y$.
The quadrants are numbered anticlockwise, starting top right.
Points and shapes
Three corners of a rectangle are $(-2, 1)$, $(4, 1)$ and $(4, -3)$. Find the fourth corner.
In which quadrant is $(-4, 6)$?
$x < 0$, $y > 0$.
In which quadrant is $(5, -2)$?
$x > 0$, $y < 0$.
The point $(0, -5)$ lies:
$x = 0$ means it is on the $y$-axis.
A rectangle has corners $(-2, 1)$, $(4, 1)$, $(4, -3)$. Enter the fourth corner as x, y.
$(-2, -3)$.
How far apart are $(2, 3)$ and $(9, 3)$?
Same $y$, so subtract the $x$-values.
How far apart are $(1, -5)$ and $(1, 3)$?
$3 - (-5)$.
Start at the origin, move 3 left and 4 up. Enter the point as x, y.
Left is negative $x$.
Which point is in the 3rd quadrant?
Both coordinates negative.
New numbers every time. Keep going until you get five in a row.