Question

answer a rotation 90° clockwise about the origin a rotation 90° counterclockwise about the origin a translation 4 units left and 5 units down a translation 5 units left and 4 units down submit answer figure j figure k

Explanation:

Step1: Recall transformation rules

For a 90 - degree clock - wise 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 rotation

Let's take a point on Figure J, say $(3,0)$.

• For 90 - degree clock - wise rotation about the origin: $(0,-3)$.
• For 90 - degree counter - clockwise rotation about the origin: $(0,3)$.

Step3: Check translation

If we consider a translation of 5 units left and 4 units down for a point $(x,y)$ on Figure J, for example, if we take the point $(3,0)$ on Figure J, the new point is $(3 - 5,0 - 4)=(-2,-4)$. If we take the point $(5,4)$ on Figure J, the new point is $(5 - 5,4 - 4)=(0,0)$. This matches the points on Figure K.

Answer:

A translation 5 units left and 4 units down