Question

the coordinates of the vertices of △jkl are j(3, 4), k(3, 1), and l(1, 1). the coordinates of the vertices of △jkl are j(-3,-5), k(-3,-2), and l(-1,-2). drag and drop the answers into the boxes to correctly complete the statement. a sequence of transformations that maps △jkl to △jkl is a box followed by a box. rotation of 90° counterclockwise about the origin rotation of 180° about the origin translation 1 unit down translation 1 unit left

Explanation:

Step1: Check rotation rules

For a point $(x,y)$ rotated 180° about the origin, the new - point is $(-x,-y)$. For point $J(3,4)$, after 180° rotation about the origin, it becomes $(-3, - 4)$. For point $K(3,1)$, it becomes $(-3,-1)$. For point $L(1,1)$, it becomes $(-1,-1)$. After 90° counter - clockwise rotation about the origin, a point $(x,y)$ becomes $(-y,x)$. This is not the case here.

Step2: Check translation after rotation

If we first rotate $\triangle JKL$ 180° about the origin, and then translate 1 unit down. For the rotated point of $J(-3,-4)$, after translating 1 unit down, it becomes $(-3,-5)$. For the rotated point of $K(-3,-1)$, after translating 1 unit down, it becomes $(-3,-2)$. For the rotated point of $L(-1,-1)$, after translating 1 unit down, it becomes $(-1,-2)$, which are the coordinates of $\triangle J'K'L'$.

Answer:

A rotation of 180° about the origin; translation 1 unit down