Basics of coordinate plane

Basics of coordinate plane

In this lesson, we will learn:

  • How to use the coordinate plane system to draw and locate points in the format (xx, yy)
  • How to rotate, reflect, and translate shapes on the coordinate plane

Notes:

  • The coordinate plane (also called coordinate system or the 2D cartesian plane/system) is a system where points on a grid are given locations called "coordinates"

  • Example: use a simple dot grid (or array) to understand how the coordinate plane works
Basics of Coordinate Plane

  • The unique and specific location of any point is given by two pieces of information
    • the column number (from left to right)
    • and the row number (from top to bottom)

  • The coordinate plane has two dimensions and points are given in the format point (x, y)
    • the location on the x-axis (from left to right, the column number)
    • and the location of the y-axis (from top to bottom, the row number)

Basics of Coordinate Plane

  • There are four types of transformations that can be done on the coordinate plane
    • Rotations: spinning shapes around a point
    • Reflections: creating a mirror image across a mirror line
    • Translations: sliding a shape (left \longleftrightarrow right) and/or (up \updownarrow down)
    • Resizing: stretching or shrinking a shape by a scale factor (i.e. doubling, halving)
Basics of Coordinate Plane

Lessons

  • 1.
    Drawing a point on the coordinate plane
    Draw a point for the coordinates given:
    a)
    (2,3)

    b)
    (8,6)

    c)
    (4,9)

    d)
    (7,5)


  • 2.
    Naming the coordinates of a point
    Write the coordinates for the point in the format (xx,yy)
    a)
    Basics of Coordinate Plane

    b)
    Basics of Coordinate Plane

    c)
    Basics of Coordinate Plane

    d)
    Basics of Coordinate Plane


  • 3.
    Translations of points on the coordinate plane
    Slide the point following the instructions. Draw the new point and write its coordinates.
    a)
    move 8 units left and 3 units up
    Basics of Coordinate Plane

    b)
    move 0 units left and 6 units down
    Basics of Coordinate Plane

    c)
    move 3 units right and 1 unit up
    Basics of Coordinate Plane


  • 4.
    Polygons and coordinate grids
    Draw and name the missing point to complete the shape
    a)
    rectangle
    Basics of Coordinate Plane

    b)
    hexagon
    Basics of Coordinate Plane

    c)
    octagon
    Basics of Coordinate Plane


  • 5.
    Basic transformations on coordinate grids
    The rectangle has points (2,7), (4,7), (2,3), (4,3)
    a)
    Translate the whole shape by sliding 5 units right and 2 units down. Draw all the points and sides after the translation. Give the coordinates of the new vertex points.
    Basics of Coordinate Plane

    b)
    Rotate the polygon 90° clockwise around the point (4,3). Draw all the points and sides after the rotation. Give the coordinates of the new vertex points.
    Basics of Coordinate Plane

    c)
    Reflect the shape across the dotted line. Draw all the points and sides after the reflection. Give the coordinates of the new vertex points.
    Basics of Coordinate Plane