Coordinate Geometry Basics: Plotting Points and Reading Graphs

1) A reliable routine for plotting any point

When you plot a point (x, y), treat the ordered pair like directions: first move horizontally to match x, then second move vertically to match y. Keeping the order consistent prevents most mistakes.

Step-by-step plotting routine

• Step 1: Start at the origin (0, 0).
• Step 2: Move along the x-direction (left/right).
  • If x is positive, move right.
  • If x is negative, move left.
  • If x = 0, do not move horizontally.
• Step 3: From that location, move along the y-direction (up/down).
  • If y is positive, move up.
  • If y is negative, move down.
  • If y = 0, do not move vertically.
• Step 4: Mark the point clearly with a dot and label it (optional but helpful in multi-point problems).

Common direction mistakes to avoid

• Switching the order: plotting (x, y) as if it were (y, x).
• Moving the correct distance but the wrong direction (e.g., treating -3 as “3 to the right” instead of “3 to the left”).
• Restarting from the origin for the y-move (the y-move starts from where the x-move ended).

2) Mixed plotting examples (integers and simple fractions)

Use the same routine for every point. Fractions simply mean “part of a unit” on the grid. If each grid square is 1 unit, then 1/2 is halfway between 0 and 1, and 3/2 is 1.5 units (one and a half squares).

Example set A: integer coordinates

Plot each point by moving in x first, then y.

• A(3, 2): from (0,0) go right 3, then up 2.
• B(-4, 1): from (0,0) go left 4, then up 1.
• C(2, -3): from (0,0) go right 2, then down 3.
• D(-1, -2): from (0,0) go left 1, then down 2.

Example set B: simple fractional coordinates

Assume the grid can be subdivided into halves (or quarters) if needed.

• E(1/2, 3): go right 1/2 (half a unit), then up 3.
• F(-2, 1/2): go left 2, then up 1/2.
• G(3/2, -1): go right 3/2 (1.5), then down 1.
• H(-1/2, -3/2): go left 1/2, then down 3/2 (1.5).

Quick self-check: re-read the point from the graph

After plotting, verify by reading the coordinates back:

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• Start at the point and look straight down/up to the x-axis to read x.
• Look straight left/right to the y-axis to read y.
• Confirm the ordered pair matches the label you intended.

3) Interpretation tasks: spotting patterns in sets of points

Graphs are not only for plotting; they also help you interpret relationships. A powerful first step is to check whether points share the same x-value or the same y-value.

Pattern A: points with the same x-value

Consider the points:

• P(2, -2)
• Q(2, 0)
• R(2, 3)

Task: What do these points have in common?

Observation: They all have x = 2.

Description in words: “All three points lie on a vertical line 2 units to the right of the y-axis.”

Graph clue: Same x-value means the points stack directly above/below each other.

Pattern B: points with the same y-value

Consider the points:

• S(-3, 1)
• T(0, 1)
• U(5/2, 1)

Task: What do these points have in common?

Observation: They all have y = 1.

Description in words: “All three points lie on a horizontal line 1 unit above the x-axis.”

Graph clue: Same y-value means the points line up left-to-right.

Pattern C: a rectangle-like “corner” pattern

Consider the points:

• V(-1, -1)
• W(3, -1)
• X(3, 2)
• Y(-1, 2)

Tasks:

• Identify pairs with the same x-value.
• Identify pairs with the same y-value.
• Describe the overall pattern.

Description in words: “These four points form the corners of a rectangle: two vertical sides at x=-1 and x=3, and two horizontal sides at y=-1 and y=2.”

4) Mini-application: connect-the-dots and verify by re-reading

You will create a simple shape by plotting points in order and connecting consecutive points with straight segments. Accuracy comes from (1) plotting carefully and (2) verifying each plotted point by reading its coordinates back from the graph.

Connect-the-dots shape: a “house” outline

Instructions: Plot the points below in order, then connect them with line segments in the same order. The last point repeats the first to close the shape.

A(0, 0) B(4, 0) C(4, 3) D(2, 5) E(0, 3) A(0, 0)

Step-by-step plotting checklist (use for each point)

• Start at the origin.
• Move to the correct x value (right for positive, left for negative).
• Move to the correct y value (up for positive, down for negative).
• Mark and label the point.

Verification: re-read each plotted point

After plotting, point to each dot and read its coordinates back from the grid. Use this table to confirm:

Accuracy checks based on patterns

• Same y-value check: A and B should both have y=0, so they should lie on the same horizontal line (the base).
• Same x-value check: B and C should both have x=4, so they should stack vertically (right wall).
• Same x-value check: A and E should both have x=0, so they should stack vertically (left wall).
• Roof symmetry idea: D has x=2, which is halfway between 0 and 4, so it should sit centered above the base.