Location and Movement, Reflection and Translation Chapter Notes | Year 5 Mathematics IGCSE (Cambridge) PDF Download

Reflection and Translation

• Reflection is a transformation where a shape is flipped over a mirror line, creating a mirror image.
• Properties of reflection:
  • The reflected shape is congruent to the original, with the same size and shape but reversed orientation.
  • Each point on the original shape is equidistant from the mirror line as its corresponding point on the reflected shape.
  • Example: Reflecting an isosceles triangle over a vertical or horizontal mirror line produces another isosceles triangle.
• Mirror lines can be vertical (parallel to the y-axis) or horizontal (parallel to the x-axis).
• Translation is a transformation where a shape is moved in a straight line without changing its size, shape, or orientation.
• Properties of translation:
  • Each vertex of the original shape moves the same distance and direction.
  • Lines connecting corresponding vertices of the original and translated shapes are parallel and of equal length.
• Comparison of reflection and translation:
  • Reflection reverses the shape’s orientation, while translation preserves it.
  • Both maintain the shape’s size and angles.
  • Reflection requires a mirror line, while translation involves a specified direction and distance.
• Some shapes can be formed by reflecting a smaller shape over two mirror lines, depending on their symmetry properties.