Learning Goal: Find the distance between two points that share an x-coordinate or a y-coordinate using absolute value.
Vocabulary
coordinateOne of the two numbers in an ordered pair (x, y).
absolute valueDistance from zero, used to keep a distance positive; |−5| = 5.
horizontalLeft-to-right direction, along the x-axis.
verticalUp-and-down direction, along the y-axis.
What You Need to Know
Two points with the same x-coordinate lie on a vertical line.
Two points with the same y-coordinate lie on a horizontal line.
For a vertical segment, the distance is the difference of the y-values.
For a horizontal segment, the distance is the difference of the x-values.
Use absolute value so the distance is always positive: |a − b|.
Subtracting a negative is the same as adding, so |3 − (−5)| = |3 + 5| = 8.
Worked Example I Do — watch how it works
Find the distance between (3, 2) and (−5, 2).
Step 1. Both points share the y-value 2, so the segment is horizontal.
Step 2. Subtract the x-values and take the absolute value: |3 − (−5)|.
Step 3. |3 + 5| = |8| = 8 units.
Answer: 8 units
Guided Practice We Do — try it together
1. Find the distance between (2, 7) and (2, 2).
💡 Hint: Same x, so subtract the y-values.
2. On a map, a park is at (−4, 1) and a school is at (6, 1). How far apart are they?
💡 Hint: Same y, so use |−4 − 6|.
3. Find the distance between (−3, −6) and (−3, −1).
💡 Hint: Same x; subtract the y-values and take absolute value.
Independent Practice You Do — show your work
1. Distance between (2, −3) and (2, 2).
2. Distance between (−6, 4) and (−1, 4).
3. Distance between (0, 8) and (0, −2).
4. A store is at (7, 5) and a home is at (7, −4). How many blocks apart are they?
5. Distance between (−5, 3) and (4, 3).
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.NS.C.8.
Item 1Selected Response6.NS.C.8
What is the distance between (−5, 2) and (3, 2)?
Select the correct answer.
Item 2Selected Response6.NS.C.8
Two points are at (4, −6) and (4, 3). What is the distance between them?
Select the correct answer.
Item 3Constructed Response6.NS.C.8
A bench is at (−3, 5) and a fountain is at (−3, −2). Find the distance between them.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
5 units
Independent 2
5 units
Independent 3
10 units
Independent 4
9 blocks
Independent 5
9 units
Item 1 · 6.NS.C.8
C — Same y, so distance is |−5 − 3| = |−8| = 8 units.
Item 2 · 6.NS.C.8
C — Same x, so distance is |3 − (−6)| = |9| = 9 units.
Item 3 · 6.NS.C.8
7 units (vertical) — They share x = −3, so the distance is |5 − (−2)| = 7 units.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.NS.C.8