Transformations
Choose a figure, and choose what should happen to it: reflected, rotated or moved. The drawing shows the figure before and after, and the table shows the new points.
The explanation is shown. Quick: pick a shape and reflect, rotate or move it. Advanced: your own points, more mirror lines and angles — and a check that the sides are the same length before and after.
Your numbers
Choose a shape
More options: your own points
Write the points as (x;y) with spaces between them, e.g. (1;1) (4;1) (1;3). At most 12 points.
Answer
Reflection in the y-axis
| Point | Before | After |
|---|---|---|
| A | (1 ; 1) | A′ (-1 ; 1) |
| B | (4 ; 1) | B′ (-4 ; 1) |
| C | (1 ; 3) | C′ (-1 ; 3) |
How to work it out
- 1(x ; y) → (−x ; y)Reflection in the y-axis: y stays the same, and x changes sign.
- 2A(1 ; 1) → A′(-1 ; 1)
- 3B(4 ; 1) → B′(-4 ; 1)
- 4C(1 ; 3) → C′(-1 ; 3)
- 5A′(-1 ; 1) B′(-4 ; 1) C′(-1 ; 3)After the move, the figure has the same shape and size as before — only its position has changed.
The formula
(x ; y) → (x ; −y)
Reflection in the x-axis.
(x ; y) → (−x ; y)
Reflection in the y-axis.
(x ; y) → (−y ; x)
Rotation of 90° anticlockwise about (0 ; 0).
(x ; y) → (−x ; −y)
Rotation of 180° about (0 ; 0) — the same as reflecting in both axes.
(x ; y) → (x + a ; y + b)
Translation by the vector (a ; b).
All three transformations keep the figure's shape and size: the sides are just as long, and the angles are the same.
In depth: more numbers and “what if”
The sides before and after
| Page | Before | After |
|---|---|---|
| AB | 3 | 3 |
| BC | 3.61 | 3.61 |
| CA | 2 | 2 |
More: Geometry
- PythagorasFind the missing side, set out a right angle, check whether a room is square, and find the space diagonal.
- Area and perimeterRectangle, triangle, trapezium, circle and composite shapes — area and perimeter.
- Volume and surface areaBox, cylinder, cone, sphere, pyramid, prism, pipe and frustum — also in litres.
- The circleRadius, circumference and area from one measurement — plus sector, annulus, chord and rise.
- Right triangleSine, cosine and tangent: all sides and angles from two known values.
- AnglesThe third angle in a triangle and the angle sum of a polygon.
- Points in the coordinate systemDistance, midpoint and the line between two points — drawn in.
- Similar figuresScale factor and missing sides — area is multiplied by k², volume by k³.
- Any triangleThe sine and cosine rules: find the rest from SSS, SAS, ASA or SSA.