Question

13 which rule can be used to represent each transformation? move the correct answer to each box.
$(x,y) \
ightarrow (x, -y)$
$(x,y) \
ightarrow (-y, x)$
$(x,y) \
ightarrow (x-1, y)$
\

$$\begin{tabular}{|l|l|} \\hline \\textbf{description of transformation} & \\textbf{rule of transformation} \\\\ \\hline a triangle is translated 1 unit to the left. & \\framebox(100,30){} \\\\ \\hline a square is reflected across the x-axis. & \\framebox(100,30){} \\\\ \\hline a pentagon is rotated $270^\\circ$ clockwise about the origin. & \\framebox(100,30){} \\\\ \\hline \\end{tabular}$$

Explanation:

For "A triangle is translated 1 unit to the left":

Step1: Recall translation rule

When a figure is translated \( h \) units horizontally, the \( x \)-coordinate changes by \( h \) (left translation means \( h=- 1\), right translation means \( h = 1\)) and \( y \)-coordinate remains the same. The rule for translation is \((x,y)\to(x + h,y)\). For a translation 1 unit to the left, \( h=-1\), so the rule is \((x,y)\to(x-1,y)\).

For "A square is reflected across the x - axis":

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \( x \)-axis is that the \( x \)-coordinate remains the same and the \( y \)-coordinate changes its sign. So the rule is \((x,y)\to(x,-y)\).

For "A pentagon is rotated \( 270^{\circ} \) clockwise about the origin":

Step1: Recall rotation rules

The rule for rotating a point \((x,y)\) \( 270^{\circ} \) clockwise about the origin is equivalent to rotating \( 90^{\circ} \) counter - clockwise. The rule for a \( 270^{\circ} \) clockwise rotation is \((x,y)\to(-y,x)\).

Answer:

• A triangle is translated 1 unit to the left: \((x,y)\to(x - 1,y)\)
• A square is reflected across the x - axis: \((x,y)\to(x,-y)\)
• A pentagon is rotated \( 270^{\circ} \) clockwise about the origin: \((x,y)\to(-y,x)\)