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Hey there! Ready to explore how shapes can slide, flip, and turn across a grid? Let's dive into the fun world of transformations!
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.
Our first move is a Translation, which is just a fancy word for a slide. When we translate a shape, we slide it up, down, left, or right without rotating or resizing it.
Next up is a Reflection, which is a mirror image or a flip across a line called the 'line of reflection'. Every point on the new shape is the exact same distance from this line as the original shape.
A triangle has vertices at A(1, 2), B(3, 2), and C(2, 5). If we translate this triangle 3 units to the right and 1 unit down, what are the coordinates of the new image points A', B', and C'?
- Understand that translating '3 units to the right' means we add 3 to each x-coordinate.
- Understand that translating '1 unit down' means we subtract 1 from each y-coordinate.
- Apply the rule (x + 3, y - 1) to point A(1, 2): A' becomes (1 + 3, 2 - 1) which is (4, 1).
- Apply the rule to point B(3, 2): B' becomes (3 + 3, 2 - 1) which is (6, 1).
- Apply the rule to point C(2, 5): C' becomes (2 + 3, 5 - 1) which is (5, 4).
- The final coordinates for the translated image are A'(4, 1), B'(6, 1), and C'(5, 4).
