When two points share an x or a y, the distance between them can be counted along a straight line.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Both on the same side
From (2, 1) to (7, 1) the gap is 7 − 2 = 5. Subtract the smaller from the larger.
Across zero
From (−3, 1) to (4, 1) the gap is 3 + 4 = 7. Count to zero, then onward.
Why it matters
The side lengths of a rectangle drawn on the plane are exactly these distances.
Points on the same horizontal or vertical line
From (2, 3) to (7, 3), only x changes, so the distance is 7 − 2 = 5. From (2, 3) to (2, −1), only y changes, so the distance is 3 − (−1) = 4. Subtract the coordinates that differ and take the absolute value.
Crossing zero
From −1 to 3 the distance is 4, which you get from 3 − (−1) = 4, or simply by counting: 1 to reach zero and 3 more. Subtracting a negative adds — a fact that is easier to accept when you can count it out on a line.
Why absolute value appears
Distance is never negative, so the subtraction is wrapped in absolute value: |7 − 2| = |2 − 7| = 5. This is why absolute value was introduced two lessons ago — it makes distance independent of the order you subtract in.
Diagonal distances come later
For two points not on the same horizontal or vertical line, this method does not work — you need Pythagoras, which arrives in Grade 8. For now, notice which pairs of points the method applies to and which it does not.
Step 2: Try It Yourself
Tap and try it out.
Step 3: Watch an Example
One step at a time.
Watch Ana Measure a Side
A rectangle has corners at (−2, 3) and (5, 3).
- Step 1
Both points have y = 3, so they lie on the same horizontal line.
Step 4: Your Turn
Practice makes it stick.
The Horizontal Gap
Problem 1 of 2
How far is it from (1, 4) to (9, 4)?
Across Zero
Problem 2 of 2
How far is it from (−4, 2) to (3, 2)?
Measure the Gap
1 of 4
Distance from (2, 5) to (2, 9)?
2 of 4
Distance from (−5, 0) to (−1, 0)?
3 of 4
Distance from (0, −3) to (0, 6)?
4 of 4
Distance from (−6, 1) to (−2, 1)?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Distance from (−3, 2) to (5, 2)?
What You Learned
- Two points sharing a coordinate lie on a straight line, so the gap can be counted.
- On the same side of zero, subtract. Across zero, add the two distances.
- These gaps are the side lengths of a polygon drawn on the plane.