# Transformations and congruent shapes · Grade 8

> Transformations and congruent shapes, Grade 8: Translation and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Transformations and congruent shapes (Grade 8) you practise 5 skills: Translation · Reflection in an axis · Congruent shapes · Rotation about the origin · Which transformation?.

A transformation moves every point of a shape to a new place. A translation, a reflection and a rotation do not change the size or the shape, so the new shape is congruent to the original one.

In a translation every point moves the same distance in the same direction. In a reflection in the x axis the y coordinate of each point changes sign, and in a reflection in the y axis the x coordinate changes sign.

In a half turn, 180° about the origin, both coordinates change sign. In a quarter turn, 90°, the two coordinates swap places, and one of them changes sign.

To find which transformation moved a shape, follow one point and check what happened to its coordinates.

**Tip:** Plot the point and its image on the grid, and check the answer by eye.

## What you learn

### Translation

- Example: The point A(8, 5) is moved 1 unit to the right and 3 units up. Where does it end up? (A coordinate grid with one point.)
- Answer: (9, 8)
- Solution: The x coordinate: 8 + 1 = 9 The y coordinate: 5 + 3 = 8 The point goes to (9, 8)

### Reflection in an axis

- Example: What is the image of the point A(6, −3) after a reflection in the x axis? (A coordinate grid with one point.)
- Answer: (6, 3)
- Solution: The x coordinate stays the same, and the y coordinate changes sign: (6, 3)

### Congruent shapes

- Example: Which two shapes are congruent? (Four shapes on a grid of squares, labelled with letters.)
- Options: 03 Shape A and shape D · 13 Shape B and shape D · 23 Shape C and shape D · 01 Shape A and shape B
- Answer: 13
- Solution: Shape B and shape D are congruent: one of them is the other after a rotation, with the same side lengths. In shape A one of the vertices has moved a square, so its side lengths are different. Shape C is twice as large: it is similar, but not congruent.

### Rotation about the origin

- Example: Rotate the point A(−6, −3) by 180° about the origin. Where does it end up? (A coordinate grid with one point.)
- Answer: (6, 3)
- Solution: Both coordinates change sign: (6, 3)

### Which transformation?

- Example: Which transformation takes the shaded triangle to the white triangle? (A coordinate grid with two triangles: a shaded triangle and a white triangle.)
- Options: A reflection in the y axis · A translation
- Answer: A reflection in the y axis
- Solution: The vertex (2, 2) goes to (−2, 2) . The x coordinate changes sign and the y coordinate stays the same, so this is a reflection in the y axis.

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education's grade 8 transition maths curriculum (2026–27).

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