Question

figure k is the result of a transformation on figure j. which transformation would accomplish this? 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

Explanation:

Step1: Recall rotation and translation rules

Rotation and translation are two - types of geometric transformations. For a 90 - degree clockwise rotation about the origin, the rule for a point $(x,y)$ is $(x,y)\to(y, - x)$. For a 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$. For a translation $a$ units left and $b$ units down, the rule for a point $(x,y)$ is $(x,y)\to(x - a,y - b)$.

Step2: Analyze the transformation from Figure J to Figure K

Let's take a point on Figure J, say the top - right vertex of Figure J which is approximately $(5,4)$. In Figure K, the corresponding vertex is approximately $(- 4,-5)$.
If we consider a 90 - degree clockwise rotation about the origin for the point $(5,4)$, we get $(4,-5)$. If we consider a 90 - degree counter - clockwise rotation about the origin for the point $(5,4)$, we get $(-4,5)$.
For a translation, if we start with a point $(x,y)$ and translate $a = 5$ units left and $b = 4$ units down, the new point is $(x - 5,y - 4)$. If $x = 5$ and $y = 4$, the new point is $(0,0)$ which is not correct. If we translate $a = 4$ units left and $b = 5$ units down, for the point $(5,4)$ we get $(5 - 4,4 - 5)=(1,-1)$ which is also not correct.
If we consider the general pattern of the transformation of all the points of Figure J to Figure K, we can see that a 90 - degree clockwise rotation about the origin will transform Figure J to Figure K.

Answer:

A rotation 90° clockwise about the origin