Neft Teacher · Learn It

Unit 7 · Standard 6.NOS.7

Ordered Pairs in All Four Quadrants

Lesson 7-8 · Learn It — how the math works

Why we're learning this

Captain Vega realized her treasure map only covered one corner of the island! She needs to expand the map in all directions — north, south, east, and west of the base camp at the origin (0, 0). Now clues can have negative coordinates: (-4, 3) means 4 units west and 3 units north. A clue at (2, -5) means 2 units east and 5 units south. Which quadrant is each clue in?

✱ Math Workbench

Learn It

How do you plot points in all four quadrants?

The coordinate plane has four parts called quadrants. A negative coordinate means you move left (for x) or down (for y) from the origin instead of right or up.

Picture itSee what the math looks like before you read about it

A colorful eight-petaled flower design sits on a coordinate grid. An orange octagon is centered on the origin O, four maroon hexagon petals point straight up, down, left, and right along the axes, and four teal petals fill the space between them.
Where you see this in real lifeA colorful eight-petaled flower design sits on a coordinate grid. An orange octagon is centered on the origin O, four maroon hexagon petals point straight up, down, left, and right along the axes, and four teal petals fill the space between them.

Watch me solve itI do — read one step at a time

The problem looks like this
A coordinate grid with (-3, -4) plotted.−5−5−4−4−3−3−2−2−1−11122334455 x y 0 (-3, -4)
  1. I will plot (-3, -4). I start at the origin (0, 0).
  2. The x is -3, which is negative, so I move 3 units to the LEFT.
  3. The y is -4, which is negative, so I move 4 units DOWN. I place my dot.
  4. Both coordinates are negative, so the point is in III.

Watch out — mistakes students make here

  • Quadrant I has both positive — you need both negative.
  • Quadrant II has negative x but positive y — check the y sign.
  • Quadrant IV has positive x — you need x negative too.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now let's plot (-5, 2). The x is -5, so which way do we move?
    Check this step
    Left 5 units.
  2. The y is 2, which is positive, so which way?
    Check this step
    Up 2 units.
  3. Left and up lands us in which ?
    Check this step
    II.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the explore, plot each treasure clue like (4, 3) and (-5, 2) and name the it lands in.

Solve: Point A is at (-5, 3). If you move 8 units to the right, what are the new coordinates?

My answer

Stuck? Open one hint at a time.

Hint 1

Moving right changes ONLY the x-coordinate. The y-coordinate stays at 3.

Hint 2

Add the move to the x-value: take -5 and count up 8. Careful crossing zero — use a number line if it helps.

Hint 3

Start at -5 and count 8 steps right: -4, -3, -2, ... keep going all 8 steps. Then keep the y as 3.

Check my answer
✅ Answer: (3, 3)
Moving right means adding to the x-coordinate: -5 + 8 = 3. The y stays the same. New point: (3, 3).

Turn & TalkSay it out loud with a partner

What do the signs of the coordinates in an ordered pair tell you about which the point is in?

Try starting with:

  • If both coordinates are positive, the point is in quadrant ___.Si ambas coordenadas son positivas, el punto esta en el cuadrante ___.
  • If the x is negative and the y is positive, the point is in quadrant ___.Si la x es negativa y la y es positiva, el punto esta en el cuadrante ___.
Use these wordsquadrantordered pairnegative coordinatex-axisy-axis