Question

write a rule to describe each transformation.
7)
8)
9)
10)
11)
12)

Explanation:

Step1: Analyze transformation 7

Count the horizontal and vertical shifts of corresponding points.

Step2: Analyze transformation 8

Check for reflection, rotation and translation by observing orientation and position of points.

Step3: Analyze transformation 9

Determine if there is a dilation along with possible rotation or translation by comparing side - lengths and angles.

Step4: Analyze transformation 10

Identify if it is a reflection across an axis by checking the orientation of the figure.

Step5: Analyze transformation 11

Look for translation by comparing the position of corresponding vertices.

Step6: Analyze transformation 12

Check for rotation around a point by observing the angle of orientation change.

Since no specific coordinates or details about the figures are given, we can't give exact rules. But in general:

• For a translation: $(x,y)\to(x + a,y + b)$ where $a$ is the horizontal shift and $b$ is the vertical shift.
• For a reflection across the $x$ - axis: $(x,y)\to(x, - y)$; across the $y$ - axis: $(x,y)\to(-x,y)$.
• For a rotation of $90^{\circ}$ counter - clockwise about the origin: $(x,y)\to(-y,x)$; $180^{\circ}$ counter - clockwise about the origin: $(x,y)\to(-x,-y)$; $270^{\circ}$ counter - clockwise about the origin: $(x,y)\to(y,-x)$.
• For a dilation with a scale factor $k$ centered at the origin: $(x,y)\to(kx,ky)$.

Answer:

Without specific details about the figures (such as coordinates of vertices), we cannot provide exact transformation rules. General rules for translations, reflections, rotations and dilations are given above.