Graphs of Ordered Pairs

Lesson 2 of 4: Data Handling

In this lesson:

• Name and locate the parts of a coordinate grid
• Plot ordered pairs in all four quadrants
• Read and describe the coordinates of any plotted point

What You Will Learn Today

1. Name the x-axis, y-axis, origin, and four quadrants on a coordinate grid
2. Plot ordered pairs of integers (including negatives) in all four quadrants
3. Read the coordinates of a plotted point; name its quadrant
4. Interpret a coordinate graph — read shape vertices, find a missing corner

Are These Two Directions the Same Address?

Imagine two people giving directions to the same park:

• Person A: "Go 3 blocks east, then 2 blocks north"
• Person B: "Go 2 blocks east, then 3 blocks north"

Do they end up at the same spot?

You Already Know Half of This

• Last lesson: two labelled axes on a travel graph
• Today: same two axes — both extended in both directions

The Parts of a Coordinate Grid

• x-axis — horizontal number line (right = positive, left = negative)
• y-axis — vertical number line (up = positive, down = negative)
• Origin — where they cross, written (0, 0)

The Four Quadrants and Their Signs

Quick Check: Name Each Grid Part

Look at the grid from the previous slide and point to each of these:

1. The y-axis
2. The origin
3. The region where and
4. The quadrant where both coordinates are negative

Name the quadrant number for item 4.

Giving Every Point a Two-Number Address

Every point has an address written (x, y):

• The first number tells you how far across (along the x-axis)
• The second number tells you how far up or down (along the y-axis)

"Along the corridor, then up the stairs"

Plotting (4, 3) — Quadrant I

• Start at the origin (0, 0)
• Move 4 right (x = +4)
• Move 3 up (y = +3) → Quadrant I

Adding (−2, 3) — Quadrant II

• −2 on the x-axis is 2 units to the left of the origin
• (Just like −2 sits left of 0 on a number line)
• Move 2 left, then 3 up → Quadrant II

Plotting Points in All Four Quadrants

• (−3, −2): 3 left, 2 down → Quadrant III
• (2, −4): 2 right, 4 down → Quadrant IV
• Negative y → move down from the x-axis

Predict First: Same Spot or Different?

Are these two points at the same location?

• Point A: (3, 2) — 3 across, 2 up
• Point B: (2, 3) — 2 across, 3 up

Predict: same spot, or different spots? Write your answer before turning the page.

Order Matters — Every Time

(3, 2) ≠ (2, 3) — different addresses, different locations

• In (3, 2): go 3 across, 2 up
• In (2, 3): go 2 across, 3 up
• The order of the numbers is not optional

Your Turn: Plot and Name

On your own grid, plot these two points:

1. A(−1, 4) — which quadrant?
2. B(3, −2) — which quadrant?

Use "corridor then stairs": across first, then up or down.

From Plotting to Reading an Address

You have learned to plot a point from its address.

Now the question flips: a point is already drawn — can you read its address?

Same move, run backwards.

How to Read a Point's Coordinates

To read the address of any plotted point:

1. Trace straight down (or up) to the x-axis — read the x-coordinate
2. Trace straight across to the y-axis — read the y-coordinate
3. Write the pair: (x, y)

The first coordinate always comes from the horizontal axis.

Points That Land on an Axis

A point on an axis has one coordinate equal to 0:

• E(0, 3) — on the y-axis; x = 0, no quadrant
• A point on the x-axis has y = 0
• Origin (0, 0) — on both axes; no quadrant

Reading Coordinates from a Five-Point Grid

Find the Error: Wrong Direction

A student plotted (−2, 3) but made a mistake.

Their point is at (2, 3) — 2 to the right, 3 up.

What did they do wrong? Where should the point actually be?

Using Coordinates as a Problem-Solving Tool

You can now plot and read any point on the grid.

Coordinates become powerful when they describe something — the corners of a shape, a route between places.

Let us put them to work.

Reading the Vertices of a Square

Four vertices of a square: P(1,1), Q(4,1), R(4,4), S(1,4)

• All four corners are in Quadrant I
• Sides PQ and SR are horizontal (same y-value)
• Sides QR and PS are vertical (same x-value)

Find the Missing Corner of the Rectangle

Three vertices of a rectangle are given: A(−2, 1), B(3, 1), C(3, −2)

Where is the fourth vertex D? Work this out on your own before looking.

Hint: A rectangle has sides that are horizontal and vertical.

Reasoning Out the Missing Vertex D

The missing vertex D shares:

• A's x-coordinate: x = −2
• C's y-coordinate: y = −2

So D = (−2, −2) — Quadrant III

Plot all four and the rectangle closes ✓

A Route on the Grid

A path goes: (0, 0) → (0, 3) → (4, 3)

In words: "3 units up, then 4 units to the right"

Coordinates describe a route — just like a travel graph

Three Things to Carry Out Today

✓ Every point has a unique address (x, y) — order is not optional

✓ Negative coordinates follow integer-line logic — left or down

✓ Coordinates are a tool: describe shapes, find missing vertices, trace routes

Next: data-03 — organising and summarising a collection of data values