Ordered Pairs on the Coordinate Plane

Ordered Pairs on the Coordinate Plane exercise

• Identify the quadrants.

  Hints

  The coordinate point is written as the $x$ coordinate first and the $y$ coordinate second. $(x, y)$

  The axes are set out like a number line with positive and negative numbers.

  $(x, y)$

  • $x$ is the horizontal axis
  • $y$ is the vertical axis

  We can see these example points are written:

  • A $= (3, 2)$
  • B $= (-2, 5)$
  • C $= (-2, -2)$
  • D $= (3, -5)$

  Solution

  • In Quadrant $1$ the $x$ and $y$ axis are positive numbers, so the coordinates are $(+, +)$.
  • In Quadrant $2$ the $x$ axis is negative and $y$ is positive, so the coordinates are $(-, +)$.
  • In Quadrant $3$ the $x$ and $y$ axis are negative numbers, so the coordinates are $(-, -)$.
  • In Quadrant $4$ he $x$ axis is positive and $y$ is negative, so the coordinates are $(+, -)$.

• Find the quadrant.

  Hints

  The quadrants are laid out like this:

  When a coordinate point has a negative $x$ and a negative $y$ we are moving left and down.

  Point $(-4, -3)$ has both negatives $(-, -)$. This means we move left for $4$ and down for $3$.

  Solution

  $(-4, -3)$ is in quadrant $3$ because both the coordinates are negative numbers $(-, -)$.

  We move left for $4$ and down for $3$, see diagram.

• Find the coordinate point.

  Hints

  To find each point:

  • first move horizontally for the $x$ coordinate.
  • second move vertically for the $y$ coordinate.

  Here is how we found coordinate A.

  • First we moved horizontally $3$ to get the $x$ coordinate.
  • Second we moved vertically $5$ to get the $y$ coordinate.
  • We would write this $(3, 5)$.

  Solution

  • A $= (3, 5)$ $3$ right, $5$ up
  • B $= (5, -3)$ $5$ right, $3$ down
  • C $= (3, -5)$ $3$ right, $5$ down
  • D $= (-3, -5)$ $3$ left, $5$ down
  • E $= (-5, 3)$ $5$ left, $3$ up

• Find the mistake.

  Hints

  The coordinate point is written across first, then up or down next.

  It looks like this $(x, y)$.

  For example, $(4, -5)$ is $4$ moves to the right from the origin and $5$ moves down from the origin.

  This point is $(-3,8)$ because the $3$ is to the left, so it’s $-3$ and the $8$ is up, so it is $+8$.

  The correct point is $(-3,8)$.

  Solution

  The mistake was at $(7, -5)$, it was $7$ left and $5$ down which is $(-7, -5)$.

  The correct ones are:

  • $(3, 2)$, $3$ right and $2$ up
  • $(4, -2)$, $4$ right and $2$ down
  • $(-2, -2)$, $2$ left and $2$ down
  • $(-3, 8)$, $3$ left and $8$ up

• Find the coordinate.

  Hints

  We write coordinates by counting the $x$ or first number across/horizontally, then the $y$ or second number up or down/vertically.

  $(x, y)$

  The $x$ coordinate is $4$ to the right and the $y$ is $2$ down.

  As a check we know it is in Quadrant $4$, so the coordinates should be in the order $(+, -)$.

  Solution

  • $(4, -2)$
  • For the $x$ coordinate (the first number), we move $4$ across/horizontally.
  • For the $y$ coordinate (the second number), we move $2$ down/vertically.
  • As a check we know it is in quadrant $4$ which has $(+, -)$ coordinates.

• Form a square using the points.

  Hints

  A square has $4$ vertices of $90^\circ$ and $4$ sides of equal length.

  We can see in this example that the red cross forms the square with the other points making the sides the same length and each vertex $90^\circ$, a right angle.

  Solution

  The correct answer is $(2, 7)$.