Test
Coordinate transformations
Dynamic tasks on translation, reflection, transformation sequences and midpoints in the coordinate plane.
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Sample questions
- Point A(___, ___) is translated by ___ units in the x-direction and ___ units in the y-direction. Find its new coordinates.
- Point A(___, ___) is reflected in the x-axis. Find the image coordinates.
- Point A(___, ___) is reflected in the y-axis. Find the image coordinates.
- Point A(___, ___) is rotated 180° about the origin. Find its new coordinates.
- Point A(___, ___) is translated twice by the same vector (___, ___). Find the final coordinates.
Coordinate transformations
A translation moves every point by the same vector: (x, y) → (x + a, y + b). Reflection in the x-axis changes the sign of y, reflection in the y-axis changes x, and reflection in the origin changes both.
Sequences of transformations
Perform operations in the stated order and use each intermediate result in the next step. The midpoint is found by averaging the x-coordinates and the y-coordinates of the endpoints.
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