Question

when describing a rotation, reflection, and translation what must be included?
translation: _____________________________
reflection: _____________________________
rotation: _____________________________

Explanation:

• Translation: A translation (slide) of a figure requires specifying the direction (e.g., horizontal, vertical, or a combination) and the distance (number of units) the figure is moved. For example, "translate 3 units to the right and 2 units up" – the direction (right, up) and distance (3, 2) are key.
• Reflection: A reflection (flip) of a figure over a line (the line of reflection) is necessary. The line of reflection can be the x - axis, y - axis, a vertical line \(x = a\), a horizontal line \(y = b\), or a diagonal line (e.g., \(y=x\)). Without the line of reflection, the reflection is not well - defined.
• Rotation: A rotation (turn) of a figure needs the center of rotation (a point around which the figure rotates, like the origin \((0,0)\) in a coordinate plane), the angle of rotation (e.g., \(90^{\circ}\), \(180^{\circ}\)), and the direction of rotation (clockwise or counter - clockwise). For example, "rotate \(90^{\circ}\) counter - clockwise about the origin" – center, angle, and direction are all required.

Answer:

• Translation: The direction (e.g., horizontal/vertical) and distance (number of units) of the move.
• Reflection: The line of reflection (e.g., x - axis, y - axis, \(y = x\) etc.).
• Rotation: The center of rotation, the angle of rotation, and the direction (clockwise/counter - clockwise) of rotation.