Transformations on a grid
Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size
What a learner can do afterwards
- Reflect a shape in a given mirror line on a grid and label the new coordinates
- Translate a shape by a given number of squares horizontally and vertically and describe the movement
- Rotate a shape 90° or 180° about a given centre on a grid and check the image is congruent to the original
1 · Read
On a grid, you can move a shape three ways: reflect it, translate it, or rotate it. Each move keeps the shape exactly the same size and shape. Only its position or the way it faces changes.
A reflection flips a shape over a mirror line. Every point of the shape moves straight across to the other side of the line, landing the same distance away. The mirror line can run up and down, side to side, or slanted diagonally, and it can even be one of the axes on a coordinate grid.
Zara slides a rectangle 4 squares right and 1 square down. The rectangle does not turn or flip: it lands in a new spot, facing the exact same way it started. That move is a translation, and you can also write it as a vector, like (4, -1).
Ben rotates a flag shape 90 degrees clockwise about the point (0, 0). Every point on the flag turns the same amount around that centre point, so the whole shape swings around, ending up the same size but facing a new direction.
To work out which transformation happened, compare the shape and its image. Check the position (has it moved?), the orientation (does it face the same way, or is it flipped or turned?), and the size (is it still exactly the same?).
Reflect flips over a mirror line, translate slides without turning, and rotate turns about a fixed point, but all three always keep the shape's size exactly the same.
More to read
Symmetry review
Symmetry is reflection hiding in plain sight. Fold a shape along its mirror line and both halves match exactly. A rectangle has 2 mirror lines, a square has 4, and an equilateral triangle has 3. Reflecting on a grid works dot by dot. Count squares from each corner to the mirror line, then plot the image the same squares past the line. The shape flips but keeps its size.
How would you describe these figures?
Describe moves with numbers, not waves of the hand. A translation of 4 right and 1 up moves every corner by the same amounts. Add 4 to each x-coordinate and 1 to each y-coordinate. Rotations need a centre and an amount. A half turn (180 degrees) about a point sends each corner to the opposite side. The image keeps every length and angle of the original.
Quadrilaterals review
Congruent shapes match exactly when stacked. Slides, flips, and turns never stretch a shape, so the image stays congruent to the original. Measure any side before and after: it stays the same. Quadrilaterals survive moves nicely. Slide a parallelogram 3 squares and it is still a parallelogram with the same sides.
Explore more
2 · Watch
به انگلیسیTake it off screen
Where it sits
Learn first
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.