Question

2.1 transformations

1. identify the transformations shown in the following graphs and write the names of the transformations in the corresponding boxes under each graph.
2. consider ab in the coordinate - plane below. the dashed line segments represent transformations of ab.

describe the transformation

Explanation:

Step1: Analyze the nature of transformation

Check for changes in position, orientation, and size of the line - segment \(AB\).

Step2: Identify translation

If only position changes without rotation, reflection or dilation, it's a translation.

Step3: Identify reflection

If the line - segment is mirrored over a line, it's a reflection.

Step4: Identify rotation

If the line - segment is turned around a point, it's a rotation.

Step5: Identify dilation

If the line - segment's length changes proportionally from a center point, it's a dilation.

Answer:

Since the graphs are not clearly visible and no specific details about the line - segments \(AB\) and their positions are given, it's not possible to provide a definite answer. However, if we assume typical coordinate - plane transformation scenarios:

1. If the line - segment moves without changing its orientation or length, it is a translation. For example, if every point \((x,y)\) on \(AB\) moves to \((x + a,y + b)\) where \(a\) and \(b\) are constants, it is a translation by the vector \(\vec{v}=(a,b)\).
2. If the line - segment is flipped over a line (such as the \(x\) - axis, \(y\) - axis, or a line \(y = x\) etc.), it is a reflection. For example, if a point \((x,y)\) on \(AB\) is transformed to \((x, - y)\), it is a reflection over the \(x\) - axis.
3. If the line - segment is rotated around a point (usually the origin \((0,0)\) or another specified point) by an angle \(\theta\), it is a rotation. Using rotation matrices, if a point \((x,y)\) is rotated counter - clockwise around the origin by an angle \(\theta\), the new coordinates \((x',y')\) are given by \(x'=x\cos\theta - y\sin\theta\) and \(y'=x\sin\theta + y\cos\theta\).
4. If the length of the line - segment changes proportionally from a fixed point (usually the origin), it is a dilation. If a point \((x,y)\) is dilated by a scale factor \(k\) with the origin as the center of dilation, the new point is \((kx,ky)\).