Neft Teacher · Learn It

Unit 7 · Standard 6.NOS.9

Determine Distance on the Coordinate Plane

Lesson 7-6 · Learn It — how the math works

Why we're learning this

Captain Vega has two treasure locations on her map: a buried chest at (-3, 2) and a hidden cave at (4, 2). Both are at the same height (y = 2) on the map. She needs to figure out how far apart they are so she knows how much rope to bring. Another pair of treasures is at (1, -3) and (1, 5) — same column, different rows. How far apart is each pair?

✱ Math Workbench

Learn It

How do you find distance on the coordinate plane?

Distance is how far apart two points are, and it is never negative. When two points share a row or a column, you can find the distance using their coordinates.

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

Tahira will walk from the middle school to the high school. The grid shows a map of the town, where each unit labeled on the grid represents one kilometer.
Where you see this in real lifeTahira will walk from the middle school to the high school. The grid shows a map of the town, where each unit labeled on the grid represents one kilometer.

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

The problem looks like this
A coordinate grid with (-3, 2) and (4, 2) plotted and joined, so the distance between them can be counted.−5−5−4−4−3−3−2−2−1−11122334455 x y 0 (-3, 2)(4, 2)Count the units along the dashed line to find thedistance.
  1. I will find the from (-3, 2) to (4, 2). Both have y = 2, so they sit on the same horizontal line.
  2. The points are on opposite sides of zero, so I add the .
  3. |-3| = 3 and |4| = 4.
  4. I add: 3 + 4 = 7. The between them is 7 units.3 + 4 = 7

Watch out — mistakes students make here

  • The x-values match — find the gap between the y-values.
  • Count from -2 up to 5 on the y-axis — don't skip zero.
  • Find |5 − (-2)| — recount the distance between -2 and 5.

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

Same steps, new numbers.

  1. Now let's find the from (2, 3) to (2, 8). What do these points share?
    Check this step
    The same x = 2, so it is a vertical line.
  2. These points are on the SAME side of zero (both positive), so do we add or subtract?
    Check this step
    We subtract.
  3. The is |8 - 3| = 5 units. When points sit on the same side of zero, subtract to find the distance.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the explore, plot each treasure pair like the Chest and Cave, then find the between them.

Solve: Two points are at (-3, -7) and (-3, 5). What is the between them?

My answer

Stuck? Open one hint at a time.

Hint 1

Both points share x = -3, so this is a vertical distance between y = -7 and y = 5.

Hint 2

The y-values have opposite signs, so add their absolute values instead of just subtracting the digits.

Hint 3

Count from -7 up to 0 (that's 7 units), then from 0 up to 5. Add the two counts.

Check my answer
✅ Answer: 12 units
Same x = -3. Distance = |5 - (-7)| = |5 + 7| = 12 units.

Turn & TalkSay it out loud with a partner

Two points sit on the same horizontal line: (2, 3) and (7, 3). How can you find the between them without counting every square?

Try starting with:

  • The y-coordinates are the same, so I only compare the ___.Las coordenadas y son iguales, asi que solo comparo las ___.
  • The distance is ___ because 7 - 2 = ___.La distancia es ___ porque 7 - 2 = ___.
Use these wordsdistancecoordinate planeabsolute valueordered pairx-axis