These questions ask you to locate points, complete or measure simple shapes on a coordinate grid, and count line or rotational symmetry for named shapes. Decide first whether you are working with positions, distances, area, folds or turns.
Read and calculate with coordinate pairs
In a pair such as (4, 7), the first number gives the horizontal position and the second gives the vertical position. The origin is (0, 0). For an axis-aligned rectangle, corners share horizontal or vertical values, so a missing corner combines the unused x-value with the unused y-value. For example, corners (2, 1), (8, 1) and (8, 5) require (2, 5).
Find a horizontal or vertical length by subtracting matching coordinates: from y equals 2 to y equals 11 is 9 units. A midpoint averages each coordinate; the midpoint of (1, 6) and (7, 6) is (4, 6). Rectangle area is width times height, and a right triangle with perpendicular base 8 and height 3 has area 12 units of area because it occupies half the matching rectangle.
Separate folds from turns
| Named shape | Symmetry facts |
|---|---|
| Rectangle with four equal sides | 4 lines of symmetry. |
| Rectangle with unequal adjacent sides | 2 lines of symmetry. |
| Triangle with three equal sides | 3 lines of symmetry and rotational symmetry of order 3. |
| Regular polygon with n sides | n lines of symmetry. A regular hexagon has 6. |
| Parallelogram that is neither a rectangle nor a rhombus | No lines of symmetry, but rotational symmetry of order 2. |
Common traps
| Tempting route | How to reject it |
|---|---|
| Read the vertical number first | Coordinate order is fixed. Swapping the two numbers usually moves the point. |
| Start the grid count at one | The axes meet before any movement, so both coordinates at the origin are zero. |
| Count touched grid points as a segment length | Distance counts the gaps between positions. Subtract the end coordinates. |
| Add endpoint coordinates to find a midpoint | A midpoint must stay between the ends. Average each pair of matching coordinates. |
| Count a mirror line twice or use a turn count as a line count | A fold line remains one line from either direction, and turning is a different symmetry test. |
Try it
Three corners of a rectangle drawn on a coordinate grid are (1, 1), (6, 1) and (6, 4), and its sides run along the grid lines. What is the fourth corner?
- (4, 1)
- (1, 6)
- (4, 6)
- (1, 4)
A rectangle on a coordinate grid has corners at (1, 2), (9, 2), (9, 5) and (1, 5). Enter the number of square units in its area.
A rectangle measures 8 centimetres by 3 centimetres, so it is not a square. Select all the statements that are true about its lines of symmetry.
- It has exactly 2 lines of symmetry.
- It has 4 lines of symmetry, because it has four right angles just as a square does.
- Neither of its diagonals is a line of symmetry.
- Folding it along a diagonal makes the two halves match exactly.