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Maths · Grade 6 · Set B
Distance on the Grid
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B
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Goal: 15 min
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Remember: Same side of zero, subtract. Opposite sides of zero, add. A distance is never negative.

Count the steps

1
P and Q have the same second number. How far apart are P and Q?
2
P and Q have the same first number. How far apart are they?
3
P is at (−1, 5) and Q is at (−7, 5). How far apart are they?
6 units8 units−6 units4 units
4
P and Q are on opposite sides of the y-axis. How far apart are they?

Same side, or opposite sides?

5
C is at (−3, 4) and D is at (−3, −1). C and D are 5 units apart.
TrueFalse
6
Each pair of points is joined by a letter pair. Which two points are 8 units apart?
A and BC and DE and F
7
Join each pair of points to how far apart they are.
  1. 1(1, 3) and (1, 11)
  2. 2(−4, 2) and (5, 2)
  3. 3(−7, −3) and (−7, −10)
  4. 4(0, −6) and (0, 4)
  • A8
  • B7
  • C10
  • D9
8
On a map each square is 1 block. The school S and the pool W are on one street. How many blocks is it from S to W?

Think it through

9
Point R is at (−3, 2). Point S is straight below R, 6 units away. What is the second number of S?
10
P is at (−6, −2) and Q is at (4, −2). Which sum or difference gives how far apart they are?
6 − 46 + 44 − 66 × 4
11
A is at (5, 4). B is in the same row, 11 units away, and to the left of the y-axis. What is the first number of B?
12
Number the steps to find how far apart (−4, 2) and (3, 2) are.
  • They are on opposite sides, so add: 4 + 3
  • Check that the second numbers match, so the points are on one flat line
  • See where each first number is: −4 is left of zero and 3 is right of zero
  • Write the distance, 7 units
13
P is at (−2, −7) and Q is at (−2, −1). Write how you find how far apart they are.
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Answer key · Set B
Distance on the Grid
15 Both points are at height 4. Only the first numbers differ: 7 less 2 is 5.
27 They sit in one column. Only the second numbers differ: 8 less 1 is 7.
36 units Both first numbers are negative, so they are on the same side of zero. Subtract: 7 − 1 = 6. A distance is never negative.
411 P is 5 left of zero and Q is 6 right of zero. Opposite sides, so add: 5 + 6 = 11.
5True C is 4 above zero and D is 1 below zero. They are on opposite sides of zero, so add: 4 + 1 = 5.
6E and F E is 6 left of zero and F is 2 right of zero: 6 + 2 = 8. A and B are 4 apart and C and D are 6 apart.
71-A, 2-D, 3-B, 4-C Same side of zero: subtract. Opposite sides: add.
810 S is 6 left of zero and W is 4 right of zero: 6 + 4 = 10 blocks.
9-4 Going down 6 from 2: 2 steps reach zero and 4 more go below it. S is at (−3, −4).
106 + 4 They are on opposite sides of zero, so you add how far each one is from zero: 6 + 4.
11-6 Going left 11 from 5: 5 steps reach zero and 6 more go past it. B is at (−6, 4).
123, 1, 2, 4 Check the line, check the sides of zero, then add or subtract.
13Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.