The coordinates of the vertices of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) .

The coordinates of the vertices of △R′S′T′ are R′(1, −2) , S′(1, 0) , and T′(5, −3) .

What is the sequence of transformations that maps △RST to △R′S′T′?

Drag and drop the answers into the boxes to correctly complete the statement.

A sequence of transformations that maps △RST to △R′S′T′ is a _followed by a ____.

-reflection across y axis
-translation 1 unit up
-rotation of 180 degress about the orgin
-rotation of 90 degrees counterclockwise about the orgin

A sequence of transformations that maps △RST to △R′S′T′ is a rotation of 90 degrees counterclockwise about the origin followed by a translation 1 unit up.

Step-by-step explanation:

It is given that the coordinates of the vertices of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5).

The coordinates of the vertices of △R′S′T′ are R′(1, −2) , S′(1, 0) , and T′(5, −3).

If △RST rotated 90 degrees counterclockwise about the origin, then

[tex](x,y)\rightarrow (-y,x)[/tex]

The vertices after rotation are

[tex]R(-3,-1)\rightarrow R_1(1,-3)[/tex]

[tex]S(-1,-1)\rightarrow S_1(1,-1)[/tex]

[tex]T(-4,-5)\rightarrow T_1(5,-4)[/tex]

After that if the image translated 1 units up then

[tex](x,y)\rightarrow (x,y+1)[/tex]

The vertices after rotation followed by translation are

[tex]R_1(1,-3)\rightarrow R'(1,-2)[/tex]

[tex]S_1(1,-1)\rightarrow S'(1,0)[/tex]

[tex]T_1(5,-4)\rightarrow T'(5,-3)[/tex]

Therefore, a sequence of transformations that maps △RST to △R′S′T′ is a rotation of 90 degrees counterclockwise about the origin followed by a translation 1 unit up.