Question

question
figure s is the result of a transformation on figure r. which transformation would accomplish this?
answer
a rotation 90° clockwise about the origin
a translation 2 units left and 3 units down
a translation 3 units left and 2 units down
a rotation 90° counterclockwise about the origin
submit answer

Explanation:

Step1: Analyze rotation rules

For a 90 - degree clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$. For a 90 - degree counter - clockwise rotation about the origin, the rule is $(-y,x)$. For a translation $a$ units left and $b$ units down, the rule for a point $(x,y)$ is $(x - a,y - b)$.

Step2: Check translation options

If we consider the translation options:

• For a translation 2 units left and 3 units down, the rule is $(x,y)\to(x - 2,y - 3)$.
• For a translation 3 units left and 2 units down, the rule is $(x,y)\to(x - 3,y - 2)$. By observing the figure, we can see that the orientation of the figure has changed, so it is not a simple translation.

Step3: Check rotation options

If we consider a 90 - degree clockwise rotation about the origin: assume a point $(x,y)$ on Figure $R$, after a 90 - degree clockwise rotation, it becomes $(y,-x)$. By observing the orientation of Figure $R$ and Figure $S$, we can see that a 90 - degree clockwise rotation about the origin will transform Figure $R$ to Figure $S$.

Answer:

A. A rotation 90° clockwise about the origin