Cartesian coordinates questions with answers

Questions

1. Question 1Read the coordinates of a point

   Write down the coordinates of the point $E$.

   Show the worked solution

   1. Step 1: Go across from the origin first: the x-coordinate (left of the origin is negative)$x = -4$
   2. Step 2: Then up or down: the y-coordinate (below the origin is negative)$y = -1$So $E(-4, -1)$.
2. Question 2Find the point (across first)

   Which point has coordinates $(-3, 2)$?

   Show the worked solution

   1. Step 1: The first number tells you how far acrossGo across $-3$ on the $x$-axis, then up $2$.
   2. Step 2: Go across, then up or down. The point there is$\text{B}$
3. Question 3The fourth corner of a shape

   $ABCD$ is a rectangle. The points $A$, $B$ and $C$ are shown. Find the coordinates of $D$.

   Show the worked solution

   1. Step 1: D is the same move from A as C is from B. Read B and C off the grid: the move from B to CAcross: $3 - 3 = 0$Up: $1 - (-5) = 6$
   2. Step 2: Make the same move from A$x = 0$$y = 1$So $D(0, 1)$.
4. Question 4Length of a horizontal or vertical line

   $P$ is the point $(-1, -2)$ and $Q$ is the point $(-1, 0)$. Find the length of $PQ$.

   Show the worked solution

   1. Step 1: Which coordinate is the same for P and Q?P and Q have the same x-coordinate, so PQ is vertical.
   2. Step 2: Subtract the coordinates that are different: larger − smaller$\mathstrut 0 - (-2) =$ $2$ units$PQ = 2$ units