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Geometric Sense
Lesson 12
Location
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ALPObjective:

Location

In this lesson you will identify and describe the location of objects on a coordinate grid in any of the four quadrants.

Vocabulary:

If you need to check a word's definition, please go to the glossary by clicking the Vocabulary button

  • angle
  • Cartesian plane
  • equilateral
  • hexagon
  • isosceles
  • octagon
  • parallelogram
  • pentagon
  • perpendicular
  • quadrilateral
  • quadrant
  • rhombus
  • right angle
  • trapezoid
  • vertex (vertices)
  • prism

Tips to Remember:

Parts of a Coordinate Grid
  • The x-axis is the horizontal number line.
  • The y-axis is the vertical number line.
  • Where the x and y-axis meet is called the origin, with coordinates of (0,0).
  • There are 4 quadrants on a coordinate grid.
  • Quadrant I includes all number pairs that have x and y both positive.
  • Quadrant II includes all number pairs that have x as being negative and y is positive.
  • Quadrant III includes all number pairs that have x as being negative and y is negative.
  • Quadrant IV includes all number pairs that have x as being positive and y is negative.
Ordered Pairs

An ordered pair is a pair of numbers placed inside parentheses with a comma between them. For example: (2,-3)

When locating points on a grid, the first coordinate, in the above ordered pair it would be 2, is called the x-coordinate. This means begin at 0, the origin where the x and y axis meet, and go to the 2 point.

The second number in the ordered pair is the y-coordinate. This means you will go -3, down three places, from the 2.

The point (2,-3) is represented on the chart.

Locating Points on a Grid

If you are given an ordered pair or coordinates to locate on a grid follow these steps:

  • Look at the first coordinate which is your x-coordinate.
  • Locate the origin of your grid, (0,0), where the x and y-axis meet.
  • Go to the point for your x-coordinate. If the number is positive you will go to the right of 0 and if the number is negative you will go to the left of 0.
  • Look at the second coordinate which is your y-coordinate.
  • From x-coordinate where you are, go up or down according to your y-coordinate. If your y-coordinate is positive you will go up that number and if it is negative you will go down that number.

For example - Locate (4, -2) on the grid.

  • Step 1: Your x-coordinate is 4.
  • Step 2: Find (0,0) on the grid.
  • Step 3: From the origin, (0,0), move to the right to the 4 mark.
  • Step 4: Your y-coordinate is -2.
  • Step 5: From the 4 on the x-axis, move down to the -2 mark. Remember, because our coordinate is negative you go down.
Your answer would look like this:
If you are given a point on a grid and need to give its ordered pair or coordinates follow these steps:
  • Find the x-coordinate first, by finding the point and going down or up until you meet the x-axis. The point you come to on the x-axis will be your x-coordinate.
  • Find the y-coordinate by finding the point and going across until you meet the y-axis. The point you come to on the y-axis will be your y-coordinate.
For example - what are the coordinates of point A?

Begin at the origin, (0,0) to help you find your x-coordinate. In this case, you move over from point (0,0) and go to the left until you come to -3 which is the number of units (on the negative side of the origin) from (0,0). That is our x-coordinate.

For the y-coordinate you go up or down from your x-coordinate. In this case, you will begin at -3, your x-coordinate, and move up until you reach your point A. From the point on the x axis you go up 5 units. Therefore, you have found your y-coordinate, 5.

Point A is labeled as (-3,5).

Understanding a Number Line

A number line is a line that shows numbers in order. Using a number line you are able determine the distance between any two integers. Below is a sample number line.

Example 1 >>

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