Question

graph the image of the figure using the transformation given.

1. rotation 90° counterclockwise about the origin
2. translation: 4 units right and 1 unit down
3. translation: 1 unit right and 1 unit up
4. reflection across the x - axis

write a rule to describe each transformation.
5)
6)

Explanation:

Step1: Recall transformation rules

• 90° counter - clockwise rotation about origin: $(x,y)\to(-y,x)$.
• Translation $(a,b)$: $(x,y)\to(x + a,y + b)$.
• Reflection across x - axis: $(x,y)\to(x,-y)$.

Step2: Apply rules for each problem

For each figure, apply the given transformation rule to each vertex and then graph new points.

Answer:

Graphs are obtained by applying transformation rules to vertices of original figures. Rules are: 1) $(x,y)\to(-y,x)$; 2) $(x,y)\to(x + 4,y-1)$; 3) $(x,y)\to(x + 1,y + 1)$; 4) $(x,y)\to(x,-y)$. For 5) and 6), identify and apply relevant transformation rules.