Year 6: Plotting points and drawing shapes
Part of the Year 6 coordinates, reflection and translation chapter. Chapter overview · whole chapter on one page
Plotting points and drawing shapes
To plot a point, start at the origin. Move across along the x-axis first, then move up or down the y-axis. Put a dot where you stop, and label it with its letter.
To draw a shape, plot each corner, then join the corners in order. A side that lies along a grid line has a length. Use the numbers that change. If the side crosses an axis, the two distances from the axis are added.
A rectangle has four right angles, and its opposite sides are equal. If three corners of a rectangle are known, the fourth corner can be found from the two sides you can see.
Key ideas
- Plot a point across first, then up or down.
- A side along a grid line: subtract the numbers that change, or add the distances from the axis if the side crosses it.
- In a rectangle, opposite sides are equal and every corner is a right angle.
- The fourth corner of a rectangle takes the across number of one corner and the up or down number of another.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Count the squares along the side, using only the numbers that change.
- Find the numbers that change. The two points have the same up or down number, so the side runs across.−2 and 3
- Find the length. The two points are on opposite sides of the y-axis, so add how far each one is from the y-axis.2 + 3 = 5
- Write the answer. A length is never negative.5
Check. Count the squares from (-2, 3) to (3, 3) one at a time: there are 5. ✓
Watch out. When the side crosses an axis, add the two distances from the axis. Do not subtract them.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Count the squares along the side, using only the numbers that change.
- Find the numbers that change. The two points have the same up or down number, so the side runs across.1 and 4
- Find the length. The two points are on the same side of the axis, so take the smaller distance away from the bigger one.4 − 1 = 3
- Write the answer. A length is never negative.3
Check. Count the squares from (1, 1) to (4, 1) one at a time: there are 3. ✓
Watch out. When the side crosses an axis, add the two distances from the axis. Do not subtract them.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Use the two sides you can see to find the corner that completes the rectangle.
- Find the horizontal side. (4, 2) and (-3, 2) have the same up or down number, so they are joined by a side across the grid.up or down number = 2
- Find the vertical side. (4, 2) and (4, -1) have the same across number, so they are joined by a side up or down the grid.across number = 4
- Find the missing corner. It takes the across number of (-3, 2) and the up or down number of (4, -1).across −3, up or down −1
- Write the answer. The fourth corner completes the rectangle.(-3, -1)
Check. (4, 2), (-3, 2), (-3, -1) and (4, -1) make a rectangle, with opposite sides the same length. ✓
Watch out. Do not copy one of the corners you were given. The missing corner is a new point.
Watch out
Common mistake: taking the length of a side that crosses an axis by subtracting the two numbers. For example, from -2 to 3 is 2 + 3 = 5 squares, not 3 - 2 = 1 square. Also, a corner you were given is never the missing corner.
Exercise 11B Practice: plotting, lengths and missing corners
Non-calculatorKey words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.
Method. Read the across number first, then the up or down number, from the origin for point A.
- Start at the origin. The origin is (0, 0), where the two axes cross.(0, 0)
- Read the across number first. Move across along the x-axis. Move left if the number is negative.x = −4
- Read the up or down number. Move up along the y-axis. Move down if the number is negative.y = −1
- Write the coordinates. Always write the across number first, then the up or down number.(-4, -1)
Check. Check on the grid: the point is 4 squares left of the y-axis, and it is 1 square down from the x-axis. ✓
Watch out. Across is always the first number. Do not swap the two numbers.
Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.
Method. Read the across number first, then the up or down number, from the origin for point B.
- Start at the origin. The origin is (0, 0), where the two axes cross.(0, 0)
- Read the across number first. Move across along the x-axis. Move left if the number is negative.x = 1
- Read the up or down number. Move up along the y-axis. Move down if the number is negative.y = −1
- Write the coordinates. Always write the across number first, then the up or down number.(1, -1)
Check. Check on the grid: the point is 1 square right of the y-axis, and it is 1 square down from the x-axis. ✓
Watch out. Across is always the first number. Do not swap the two numbers.
Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.
Method. Read the across number first, then the up or down number, from the origin for point C.
- Start at the origin. The origin is (0, 0), where the two axes cross.(0, 0)
- Read the across number first. Move across along the x-axis. Move left if the number is negative.x = 1
- Read the up or down number. Move up along the y-axis. Move down if the number is negative.y = 1
- Write the coordinates. Always write the across number first, then the up or down number.(1, 1)
Check. Check on the grid: the point is 1 square right of the y-axis, and it is 1 square up from the x-axis. ✓
Watch out. Across is always the first number. Do not swap the two numbers.
Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.
Method. Read the across number first, then the up or down number, from the origin for point D.
- Start at the origin. The origin is (0, 0), where the two axes cross.(0, 0)
- Read the across number first. Move across along the x-axis. Move left if the number is negative.x = −4
- Read the up or down number. Move up along the y-axis. Move down if the number is negative.y = 1
- Write the coordinates. Always write the across number first, then the up or down number.(-4, 1)
Check. Check on the grid: the point is 4 squares left of the y-axis, and it is 1 square up from the x-axis. ✓
Watch out. Across is always the first number. Do not swap the two numbers.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Count the squares along the side, using only the numbers that change.
- Find the numbers that change. The two points have the same up or down number, so the side runs across.−4 and 1
- Find the length. The two points are on opposite sides of the y-axis, so add how far each one is from the y-axis.4 + 1 = 5
- Write the answer. A length is never negative.5
Check. Count the squares from (-4, -1) to (1, -1) one at a time: there are 5. ✓
Watch out. When the side crosses an axis, add the two distances from the axis. Do not subtract them.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Count the squares along the side, using only the numbers that change.
- Find the numbers that change. The two points have the same across number, so the side runs up or down.−1 and 1
- Find the length. The two points are on opposite sides of the x-axis, so add how far each one is from the x-axis.1 + 1 = 2
- Write the answer. A length is never negative.2
Check. Count the squares from (1, -1) to (1, 1) one at a time: there are 2. ✓
Watch out. When the side crosses an axis, add the two distances from the axis. Do not subtract them.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Add the lengths of all four sides.
- Write the lengths of the four sides. A rectangle has two long sides and two short sides.5, 2, 5 and 2
- Add the four sides. The perimeter is the distance all the way round.5 + 2 + 5 + 2 = 14
- Write the answer. The perimeter is in squares, one for each unit of length.14
Check. 2 × (5 + 2) = 14. ✓
Watch out. Count all four sides, not just the two you can see first.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Use the two sides you can see to find the corner that completes the rectangle.
- Find the horizontal side. (2, 1) and (7, 1) have the same up or down number, so they are joined by a side across the grid.up or down number = 1
- Find the vertical side. (2, 1) and (2, 5) have the same across number, so they are joined by a side up or down the grid.across number = 2
- Find the missing corner. It takes the across number of (7, 1) and the up or down number of (2, 5).across 7, up or down 5
- Write the answer. The fourth corner completes the rectangle.(7, 5)
Check. (2, 1), (7, 1), (7, 5) and (2, 5) make a rectangle, with opposite sides the same length. ✓
Watch out. Do not copy one of the corners you were given. The missing corner is a new point.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Use the two sides you can see to find the corner that completes the rectangle.
- Find the horizontal side. (-1, -2) and (-6, -2) have the same up or down number, so they are joined by a side across the grid.up or down number = −2
- Find the vertical side. (-1, -2) and (-1, 3) have the same across number, so they are joined by a side up or down the grid.across number = −1
- Find the missing corner. It takes the across number of (-6, -2) and the up or down number of (-1, 3).across −6, up or down 3
- Write the answer. The fourth corner completes the rectangle.(-6, 3)
Check. (-1, -2), (-6, -2), (-6, 3) and (-1, 3) make a rectangle, with opposite sides the same length. ✓
Watch out. Do not copy one of the corners you were given. The missing corner is a new point.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Use the two sides you can see to find the corner that completes the rectangle.
- Find the horizontal side. (1, -2) and (-2, -2) have the same up or down number, so they are joined by a side across the grid.up or down number = −2
- Find the vertical side. (1, -2) and (1, 1) have the same across number, so they are joined by a side up or down the grid.across number = 1
- Find the missing corner. It takes the across number of (-2, -2) and the up or down number of (1, 1).across −2, up or down 1
- Write the answer. The fourth corner completes the rectangle.(-2, 1)
Check. (1, -2), (-2, -2), (-2, 1) and (1, 1) make a rectangle, with opposite sides the same length. ✓
Watch out. Do not copy one of the corners you were given. The missing corner is a new point.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Count the squares along the side, using only the numbers that change.
- Find the numbers that change. The two points have the same across number, so the side runs up or down.−1 and 4
- Find the length. The two points are on opposite sides of the x-axis, so add how far each one is from the x-axis.1 + 4 = 5
- Write the answer. A length is never negative.5
Check. Count the squares from (2, -1) to (2, 4) one at a time: there are 5. ✓
Watch out. When the side crosses an axis, add the two distances from the axis. Do not subtract them.
Key words. The origin is the point (0, 0), where the x-axis and the y-axis cross. A coordinate is a pair of numbers (x, y). The x-value is the across number, and it is always written first.
Method. Look at each corner, one at a time, and check the sign of each number.
- Check the first corner. The corner (2, 2) has a positive across number and a positive up number.2 > 0 and 2 > 0
- Check the other corners. The other corners are (5, 2), (5, 6) and (2, 6). They are all positive too.all positive
- Decide. All the corners are in the first quadrant, so the whole rectangle is there.Yes
Check. Positive across numbers are right of the y-axis, and positive up numbers are above the x-axis. ✓
Watch out. A shape is in one quadrant only if every corner is in that quadrant.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Find the width and the height of the rectangle, then multiply them.
- Find the width. The points (-5, 0) and (-2, 0) lie on the same line, so the side is 3 squares long.3 squares
- Find the height. The points (-2, 0) and (-2, 3) lie on the same line, so the side is 3 squares high.3 squares
- Multiply the width by the height. Each row has 3 squares, and there are 3 rows.3 × 3 = 9
- Write the answer. 9 squares
Check. Counting the squares row by row: 3 + 3 + 3 = 9. ✓
Watch out. Count the squares inside the shape, not the corners.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Count the squares along the side, using only the numbers that change.
- Find the numbers that change. The two points have the same across number, so the side runs up or down.3 and −4
- Find the length. The two points are on opposite sides of the x-axis, so add how far each one is from the x-axis.3 + 4 = 7
- Write the answer. A length is never negative.7
Check. Count the squares from (-2, 3) to (-2, -4) one at a time: there are 7. ✓
Watch out. When the side crosses an axis, add the two distances from the axis. Do not subtract them.
Key words. The perimeter is the distance all the way round the outside of a shape. A rectangle has four right angles, and its opposite sides are equal.
Method. Use the two sides you can see to find the corner that completes the rectangle.
- Find the horizontal side. (2, 3) and (-4, 3) have the same up or down number, so they are joined by a side across the grid.up or down number = 3
- Find the vertical side. (2, 3) and (2, -1) have the same across number, so they are joined by a side up or down the grid.across number = 2
- Find the missing corner. It takes the across number of (-4, 3) and the up or down number of (2, -1).across −4, up or down −1
- Write the answer. The fourth corner completes the rectangle.(-4, -1)
Check. (2, 3), (-4, 3), (-4, -1) and (2, -1) make a rectangle, with opposite sides the same length. ✓
Watch out. Do not copy one of the corners you were given. The missing corner is a new point.