Coordinate Planes and Ordered Pairs

Coordinate Planes and Ordered Pairs exercise

• Identify a co-ordinate of the vertex of a given shape.

  Hints

  What properties do you know about rectangles?

  • They have 4 right angles.
  • The opposite sides are parallel and equal to each other
  • They are quadrilaterals and have 4 sides

  When plotting a co-ordinate, the $x$ value comes first and then the $y$ value comes second. So a co-ordinate of $(4, 10)$ would be 4 across on the $x$ axis and then 10 up on the $y$ axis.

  Coordinates are given as ordered pairs. The first number is the $x$ coordinate, which describes the horizontal position. The second number is the $y$ coordinate, which describes the vertical position.

  Solution

  The correct co-ordinate to complete the rectangle is $(8,7)$. As you can see on the axes now, by plotting this co-ordinate the rectangle has all the properties which make it correct!

• Identify the locations of different co-ordinates on a graph.

  Hints

  Remember, co-ordinates are plotted $x$ first and then $y$ second. This means you move vertically the $x$ amount first, and then horizontally the $y$ amount after. You might also know this as the saying "along the corridor and up the stairs!" as another easy way to remember how to plot co-ordinates.

  A co-ordinate of $(4,3)$ would be plotted by moving 4 across horizontally to the right on the $x$-axis, and then 3 vertically upwards on the $y$-axis.

  A co-ordinate of $(-5,-1)$ would be plotted by moving 5 across horizontally to the left on the $x$-axis, and then 1 vertically downwards on the $y$-axis.

  Solution

  The places you should have highlighted that the pirates needed to check for the treasures, are $(2,2)$ - the shipwreck, $(-7,7)$ - the jungle, $(-3,-7)$ - the kraken, $(7,8)$ - the skull cave and finally, $(2,-3)$ - the mermaid rock!

• Complete the passage of text.

  Hints

  Two lines that cross one another at 90-degrees are called perpendicular lines.

  The $x$-axis is the horizontal axis and the $y$-axis is the vertical axis.

  The point $(0,0)$ is called the origin.

  Plotting co-ordinates can be helpful with graphing equations and mapping locations.

  Solution

  In mathematics, plotting coordinates helps us locate points on a grid. A co-ordinate grid has two perpendicular lines: the horizontal $x$-axis and the vertical y-axis. The intersection point of these axes is called the origin and is represented by (0,0).

  To plot a point on the grid, we use co-ordinates. The first number shows the horizontal position on the $x$-axis, and the second number shows the vertical position on the $y$-axis. These numbers form an ordered pair, with the $x$-coordinate first, the $y$-coordinate second, separated by a comma, and enclosed in brackets.

  To plot the point (3, 4), move three units right along the $x$-axis and four units up along the $y$-axis. The point (3, 4) is three units right and four units above the origin. Similarly, plot (-2, -5) by moving two units left and five units down from the origin.

  By understanding how to plot coordinates, we can graph equations, map locations, and solve various mathematical problems accurately.

• Which co-ordinates have been plotted correctly?

  Hints

  Co-ordinates should be plotted using crosses and not dots! This is because crosses allow for greater accuracy.

  Co-ordinates are plotted using the $x$ value first and then the $y$ value second.

  Take care with the scale on the axes! Students often assume the scale always goes up in one's but it can be two's, five's, ten's or any amount.

  All co-ordinates should be plotted by starting at the origin. As you get more confident with them you will get quicker at plotting them but this important fact is the basis of plotting all co-ordinates.

  Coordinates are given as ordered pairs. The first number is the $x$ coordinate, which describes the horizontal position. The second number is the $y$ coordinate, which describes the vertical position.

  Solution

  This student has confused the order of the co-ordinate! They have forgotten that a co-ordinate gives information in the order $(x,y)$. The first value is the $x$ co-ordinate value and the second value is the $y$ co-ordinate value. The $x$-axis is the horizontal axis and the $y$-axis is the vertical axis.

• Finding Stars.

  Hints

  Find the key information in the question which is relevant to the problem.

  Although the information about stars and constellation might be interesting, what key bits of information are relevant to actually answering the problem?

  A co-ordinate presents two bits of information, an $x$ co-ordinate which represents how far you move horizontally on the $x$-axis, and the $y$ co-ordinate which represents how far you move vertically on the $y$-axis.

  The $x$ co-ordinate value comes first in a co-ordinate pair, and then the $y$ co-ordinate value comes second.

  For example, the co-ordinate $(3,2)$ gives an $x$ co-ordinate value of 3, and a $y$ co-ordinate value of 2.

  Solution

  The co-ordinate plotted at the point $(5,6)$ is highlighted on the illustration showing which star is the brightest in the constellation Ursa Major.

• Identifying a co-ordinate on a graph.

  Hints

  To find halfway between two numbers, you can add them together and then divide them by 2.

  For example, to find the half way between 2 and 6, you can add them together (2 + 6) = 8, and then divide it by 2, which equals 4!

  Find half way between the two $x$ co-ordinate values, and then find half way between the two $y$ co-ordinate values.

  Halfway between the two points $(2,2)$ and $(6,4)$ is the point, $(4,3)$.

  Solution

  The new train station should be plotted at the point, $(6,7)$.