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Hey there! Ready to explore how shapes move, flip, and turn in geometry? Let's discover the magic of transformations together!
A transformation is a way of moving or changing a geometric shape. The original shape is called the 'pre-image', and the new shape after the move is called the 'image'.
The simplest move is a translation, which is just a slide! Every single point of the shape slides the exact same distance in the exact same direction without turning or flipping.
Next up is a reflection, which works just like a mirror! The shape flips across a line called the 'line of reflection' to create a backwards, matching image.
A triangle has points at A(1, 2), B(3, 2), and C(1, 5). If we translate this triangle 4 units to the right and 1 unit down, what are the coordinates of the new image points A', B', and C'?
- Identify the translation rule: '4 units right' means we add 4 to each x-coordinate, and '1 unit down' means we subtract 1 from each y-coordinate.
- Apply the rule to point A(1, 2): New x = 1 + 4 = 5. New y = 2 - 1 = 1. So, A' is (5, 1).
- Apply the rule to point B(3, 2): New x = 3 + 4 = 7. New y = 2 - 1 = 1. So, B' is (7, 1).
- Apply the rule to point C(1, 5): New x = 1 + 4 = 5. New y = 5 - 1 = 4. So, C' is (5, 4).
- Write down your final coordinates for the image: A'(5, 1), B'(7, 1), and C'(5, 4).
