Transformations and congruent shapes · Year 7
In Transformations and congruent shapes (Year 7) you practise 4 skills: Translation · Reflection in an axis · Congruent shapes · Rotation about the origin. 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
For example: The point A(8, 5) is moved 1 unit to the right and 3 units up. Where does it end up?
Answer and solution
The answer: (9, 8)
The x coordinate: 8 + 1 = 9 The y coordinate: 5 + 3 = 8 The point goes to (9, 8)
Reflection in an axis
For example: What is the image of the point A(6, −3) after a reflection in the x axis?
Answer and solution
The answer: (6, 3)
The x coordinate stays the same, and the y coordinate changes sign: (6, 3)
Congruent shapes
For example: Which two shapes are congruent?
- Shape A and shape D
- Shape B and shape D
- Shape C and shape D
- Shape A and shape B
Answer and solution
The answer: 13
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
For example: Rotate the point A(−6, −3) by 180° about the origin. Where does it end up?
Answer and solution
The answer: (6, 3)
Both coordinates change sign: (6, 3)
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).