Graphs · On the grid · 2.2

Distance on the grid.

For two points on the same horizontal or vertical line, the distance is the difference of the changing coordinates. (2, 1) to (2, 6): same x, so distance = |6 − 1| = 5.

01 / THE IDEA

See it work.

Watch the method

Distance on the grid

(2, 1) to (2, 6) → |6 − 1| = 5.

1 / 1
-6-666
1

Vertical distance

The points share an x, so subtract the other coordinates.

∣6−1∣=5|6 - 1| = 5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 5.

streak 0
best 0
-6-666
Your answer:
— / WHY IT WORKS

The idea underneath.

Subtract the difference

If the x’s match, subtract the y’s; if the y’s match, subtract the x’s. Take the absolute value.

Why it works

|6 − 1| = 5 units apart.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the distance between (2,-2) and (2,-4).

1

Vertical distance

The points share an x, so subtract the other coordinates. |-4 - -2| = 2

EX 2medium

Find the distance between (-3,-3) and (1,-3).

1

Horizontal distance

The points share a y, so subtract the other coordinates. |1 - -3| = 4

EX 3hard

Find the distance between (5,2) and (-4,2).

1

Horizontal distance

The points share a y, so subtract the other coordinates. |-4 - 5| = 9

04 / COMMON TRAPS

Where students slip.

Trap

Adding the coordinates.

Fix

Subtract to find the gap.

Trap

Forgetting the absolute value.

Fix

Distance is never negative.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Find the distance between (-4,5) and (2,5).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
C2

Find the distance between (-5,3) and (-1,3).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
C3

Find the distance between (5,-5) and (5,4).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
C4

Find the distance between (-4,-1) and (1,-1).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
Apply

Apply (4)

A1

Find the distance between (2,-1) and (2,1).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
A2

Find the distance between (5,2) and (-1,2).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
A3

Find the distance between (5,2) and (3,2).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
A4

Find the distance between (3,5) and (1,5).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
Extension

Extension (4)

E1

Find the distance between (-2,5) and (5,5).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
E2

Find the distance between (-4,-1) and (-4,-2).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
E3

Find the distance between (-5,2) and (-5,-4).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).
E4

Find the distance between (3,5) and (3,-2).

Need a hint?
  • Find which coordinate is the same.
  • Subtract the other one (absolute value).