Year 6 Maths reasoning (SATs): Missing coordinates and the centre of a shape
Part of the Year 6 Maths reasoning (SATs) position and coordinates chapter. Chapter overview · whole chapter on one page
Missing coordinates and the centre of a shape
Rule
The centre of a rectangle is halfway between two opposite corners: add the two x-values and halve; do the same for y.
If a rectangle has sides parallel to the axes, the missing corner uses the x-value and the y-value that appear only once.
Key ideas
- Centre = halfway between opposite corners.
- Halve the sum of the coordinates.
- Missing corner: the x-value and y-value that appear once.
Method. The centre is halfway between opposite corners.
- Add the x-coordinates of the opposite corners. 1 + 5 = 6.6
- Halve it. 6 / 2 = 3.x = 3
- Do the same for the y-coordinates. 1 + 3 = 4, and half of that is 2.(3, 2)
- Write the answer. (3, 2)
Check. The centre is halfway between (1, 1) and (5, 3). ✓
Watch out. Halve the sum of the coordinates, not the difference.
Method. Find the x-value and the y-value that appear only once.
- Look at the x-coordinates. The x-coordinates are 1, 5 and 1. One of them is the only one that appears once.x = 5
- Look at the y-coordinates. The y-coordinates are 2, 2 and 6.y = 6
- Write the fourth corner. The fourth corner uses the unpaired x and y values.(5, 6)
- Write the answer. (5, 6)
Check. The corners (1, 2), (5, 2), (1, 6) and (5, 6) make a rectangle. ✓
Watch out. The fourth corner shares its x with one corner and its y with another.
Method. The centre is halfway between opposite corners.
- Add the x-coordinates of the opposite corners. -4 + 2 = -2.-2
- Halve it. -2 / 2 = -1.x = -1
- Do the same for the y-coordinates. -2 + 6 = 4, and half of that is 2.(-1, 2)
- Write the answer. (-1, 2)
Check. The centre is halfway between (-4, -2) and (2, 6). ✓
Watch out. Halve the sum of the coordinates, not the difference.
Watch out
Watch out. The centre is the midpoint, not the difference. Add the coordinates, then halve.
Exam tip
Practice guide. Sketch the rectangle quickly on squared paper. The missing corner is then easy to see.
Exercise 6D Practice: missing corners and centres
Non-calculatorMethod. The centre is halfway between opposite corners.
- Add the x-coordinates of the opposite corners. 0 + 6 = 6.6
- Halve it. 6 / 2 = 3.x = 3
- Do the same for the y-coordinates. 0 + 4 = 4, and half of that is 2.(3, 2)
- Write the answer. (3, 2)
Check. The centre is halfway between (0, 0) and (6, 4). ✓
Watch out. Halve the sum of the coordinates, not the difference.
Method. The centre is halfway between opposite corners.
- Add the x-coordinates of the opposite corners. -2 + 4 = 2.2
- Halve it. 2 / 2 = 1.x = 1
- Do the same for the y-coordinates. 1 + 5 = 6, and half of that is 3.(1, 3)
- Write the answer. (1, 3)
Check. The centre is halfway between (-2, 1) and (4, 5). ✓
Watch out. Halve the sum of the coordinates, not the difference.
Method. The centre is halfway between opposite corners.
- Add the x-coordinates of the opposite corners. -6 + 2 = -4.-4
- Halve it. -4 / 2 = -2.x = -2
- Do the same for the y-coordinates. -4 + 0 = -4, and half of that is -2.(-2, -2)
- Write the answer. (-2, -2)
Check. The centre is halfway between (-6, -4) and (2, 0). ✓
Watch out. Halve the sum of the coordinates, not the difference.
Method. Find the x-value and the y-value that appear only once.
- Look at the x-coordinates. The x-coordinates are 2, 6 and 2. One of them is the only one that appears once.x = 6
- Look at the y-coordinates. The y-coordinates are 1, 1 and 5.y = 5
- Write the fourth corner. The fourth corner uses the unpaired x and y values.(6, 5)
- Write the answer. (6, 5)
Check. The corners (2, 1), (6, 1), (2, 5) and (6, 5) make a rectangle. ✓
Watch out. The fourth corner shares its x with one corner and its y with another.
Method. Find the x-value and the y-value that appear only once.
- Look at the x-coordinates. The x-coordinates are -3, -3 and 1. One of them is the only one that appears once.x = 1
- Look at the y-coordinates. The y-coordinates are -2, 4 and 4.y = -2
- Write the fourth corner. The fourth corner uses the unpaired x and y values.(1, -2)
- Write the answer. (1, -2)
Check. The corners (-3, -2), (-3, 4), (1, 4) and (1, -2) make a rectangle. ✓
Watch out. The fourth corner shares its x with one corner and its y with another.
Method. Find the x-value and the y-value that appear only once.
- Look at the x-coordinates. The x-coordinates are 0, 5 and 5. One of them is the only one that appears once.x = 0
- Look at the y-coordinates. The y-coordinates are 0, 0 and 3.y = 3
- Write the fourth corner. The fourth corner uses the unpaired x and y values.(0, 3)
- Write the answer. (0, 3)
Check. The corners (0, 0), (5, 0), (5, 3) and (0, 3) make a rectangle. ✓
Watch out. The fourth corner shares its x with one corner and its y with another.
Method. The centre is halfway between opposite corners.
- Opposite corner x. 2 x 3 - 1 = 5.5
- Opposite corner y. 2 x 3 - 1 = 5.5
- Write the corner. The opposite corner is (5, 5).(5, 5)
- Write the answer. (5, 5)
Check. (1 + 5) / 2 = 3 and (1 + 5) / 2 = 3. ✓
Method. Halve the sum of x and the sum of y.
- x. (0 + 8) / 2 = 4.4
- y. (0 + 6) / 2 = 3.3
- Write the answer. (4, 3)
Check. 4 + 4 = 8 and 3 + 3 = 6. ✓
Method. Add, then halve, for each coordinate.
- x. (-2 + 4) / 2 = 1.1
- y. (3 + (-1)) / 2 = 1.1
- Write the answer. Add the x-values, -2 + 4 = 2, halve to get 1; add the y-values, 3 + (-1) = 2, halve to get 1; the centre is (1, 1).
Check. (1, 1) is halfway between the corners. ✓
Method. Find the x-value and y-value that appear only once.
- x. x-values: -1, 3, 3. The value that appears once is -1.-1
- y. y-values: 2, 2, -4. The value that appears once is -4.-4
- Write the corner. The fourth corner is (-1, -4).(-1, -4)
- Write the answer. (-1, -4)
Check. The rectangle has corners (-1, 2), (3, 2), (3, -4) and (-1, -4). ✓
Method. Use the opposite corners.
- Use the opposite corners. The corners (0, 0) and (4, 4) are opposite.(0, 0) and (4, 4)
- Halve. (0 + 4) / 2 = 2 for x and for y.(2, 2)
- Write the answer. Because the centre is halfway between (0, 0) and (4, 4), so (0 + 4) / 2 = 2 and (0 + 4) / 2 = 2.
Check. (0 + 4) / 2 = 2. ✓
Method. Find the midpoint of opposite corners.
- Midpoint of x. (1 + 7) / 2 = 4.4
- Midpoint of y. (1 + 5) / 2 = 3.3
- Write the answer. (4, 3)
Check. (1 + 7) / 2 = 4. ✓
Method. Find the x-value and the y-value that appear only once.
- Look at the x-coordinates. The x-coordinates are -4, -4 and 3. One of them is the only one that appears once.x = 3
- Look at the y-coordinates. The y-coordinates are -4, 2 and 2.y = -4
- Write the fourth corner. The fourth corner uses the unpaired x and y values.(3, -4)
- Write the answer. (3, -4)
Check. The corners (-4, -4), (-4, 2), (3, 2) and (3, -4) make a rectangle. ✓
Watch out. The fourth corner shares its x with one corner and its y with another.