Coordinate plane review

Key Notes :

Coordinate Plane Basics:

  • The coordinate plane consists of two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical).
  • The point where the axes intersect is called the origin, denoted as (0, 0).

Coordinates:

  • Coordinates are pairs of numbers (x, y) that locate points on the plane.
  • The x-coordinate tells you how far horizontally the point is from the origin.
  • The y-coordinate tells you how far vertically the point is from the origin.

Quadrants:

  • The coordinate plane is divided into four quadrants by the axes.
  • Quadrant I: (+, +), Quadrant II: (-, +), Quadrant III: (-,-), Quadrant IV: (+, -).
  • Understanding which quadrant a point belongs to based on its coordinates.

Plotting Points:

  • To plot a point, move horizontally (x) first and then vertically (y) from the origin.
  • Example: To plot (2, 3), move 2 units to the right on the x-axis and then 3 units up on the y-axis.

Distance and Midpoint:

  • Calculating the distance between two points using the distance formula:
  • Finding the midpoint of a line segment using the midpoint formula:

Graphing Equations:

  • Graphing linear equations (y = mx + b) by plotting points or using the slope-intercept form.
  • Understanding how changes in slope (m) and y-intercept (b) affect the graph.

Reflection and Symmetry:

  • Reflecting points across the x-axis, y-axis, and origin.
  • Recognizing symmetry in graphs, such as even (y axis) and odd (origin) symmetry.

Learn with an example

What are the coordinates of point W?

Find the x-coordinate.

Start at point W and move down until you reach the x-axis.

This position on the x-axis is 5 units to the left of the origin. All x-coordinates to the left of the origin are negative.

So, the x-coordinate of point W is –5.

Find the y-coordinate.

Start at point W and move right until you reach the y-axis.

This position on the y-axis is 1 unit above the origin. All y-coordinates above the origin are positive.

So, the y-coordinate of point W is 1.

Write the coordinates.

Always write the x-coordinate first and the y-coordinate second.

The coordinates of point W are (–5,1).

What are the coordinates of point D?

Find the x-coordinate.

Start at point D and move up until you reach the x-axis.

This position on the x-axis is 5 units to the left of the origin. All x-coordinates to the left of the origin are negative.

So, the x-coordinate of point D is –5.

Find the y-coordinate.

Start at point D and move right until you reach the y-axis.

This position on the y-axis is 1 unit below the origin. All y-coordinates below the origin are negative.

So, the y-coordinate of point D is –1.

Write the coordinates.Always write the x-coordinate first and the y-coordinate second.

The coordinates of point D are (–5,–1).

Let’s practice!