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Worksheets›Grade 6›Number system›Distances and perimeter on the coordinate plane

Distances and Perimeter on the Coordinate Plane Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Grade 6CCSS 6.NS.C.8Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Points in the same quadrant

  1. 1.On a town map, the library is at (6,(6,(6, 2)2)2) and the school is at (6,(6,(6, 3).3).3). Each unit is one block. How many blocks apart are they?
  2. 2.Find the distance between (−2,(-2,(−2, 1)1)1) and (−4,(-4,(−4, 1).1).1).
  3. 3.Find the distance between (1,(1,(1, −8)-8)−8) and (1,(1,(1, −9).-9).−9).
  4. 4.Find the distance between (−1,(-1,(−1, 3)3)3) and (−6,(-6,(−6, 3).3).3).
  5. 5.Find the distance between (3,(3,(3, −2)-2)−2) and (3,(3,(3, −5).-5).−5).
  6. 6.Find the distance between (5,(5,(5, 2)2)2) and (6,(6,(6, 2).2).2).
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

When two points share an x- or a y-coordinate, the distance between them is the difference of the other coordinates. If the points are on opposite sides of an axis, that is the same as adding their distances from the axis.

EasyFind the distance between (−3,(-3,(−3, −4)-4)−4) and (−1,(-1,(−1, −4).-4).−4).Points in the same quadrantMediumOn a town map, the library is at (6,(6,(6, −1)-1)−1) and the school is at (6,(6,(6, 3).3).3). Each unit is one block. How many blocks apart are they?Points on opposite sides of an axisHardA rectangle has vertices (−6,(-6,(−6, −8),-8),−8), (−9,(-9,(−9, −8),-8),−8), (−9,(-9,(−9, 5)5)5) and (−6,(-6,(−6, 5).5).5). Find its perimeter.Perimeter of a rectangle from its vertices

How to solve it: a worked example

Find each distance or perimeter in grid units.

  1. StartOn a town map, the library is at (6,(6,(6, 6)6)6) and the school is at (6,(6,(6, 4).4).4). Each unit is one block. How many blocks apart are they?
  2. Same x-coordinate, so use the y-coordinates∣6|6∣6 −-− 4∣4|4∣ === 222
  3. Answer222

Common mistakes to watch for

  • Subtracting a negative coordinate as if it were positive: from −2 to 5 is 7, not 3.
  • Subtracting the coordinates that are the same.
  • Adding only two sides of the rectangle for the perimeter.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Dividing fractionsAdding & subtracting decimalsMultiplying decimalsDividing decimalsGreatest common factor

FAQ

What is the distance from (−3, 2) to (4, 2)?

The y-coordinates match, so use the x-coordinates: |−3 − 4| = 7. Or count 3 to the y-axis and 4 more past it.

How do you find the perimeter of a rectangle on the grid?

Find the width from the x-coordinates and the height from the y-coordinates, then add all four sides: 2 × width + 2 × height.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix distances and perimeter on the coordinate plane with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.