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 . answer choices: translation 1 unit up. rotation of 180 degrees about the origin. rotation of 90 degrees counterclockwise about the origin. reflection across the y-axis.

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

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

Solution : We know the rule for the new coordinates of rotatation 90°counterclockwise about the origin.The rule is (h, k) ---> (-k,h).

Where (h,k) are the coordinates of original image on axes and (-k,h) are the coordinates of rotated image.

In resulting coordinates of the image first swap the x and y coordinates of the original image and then make the sign opposite of each x-coordinate.

On applying rule (h, k) ---> (-k,h), we get

R(−3, −1) --> R′(1, -3).

S(−1, −1) --> S′(1, -1).

T(−4, −5)  --> T′(5, −4).

Let us apply another rule, each of the y-coordinate is getting reduced by 1 by adding 1 to the new coordinates.

Adding 1 to y-coordinates, we get

(1, -3) --> (1,-3+1) --> R'(1,-2)

(1, -1) --> (1,-1+1) --> S'(1,0) and

(5, −4) --> (5,-4+1) --> T' (5,-3).

So, the transformations steps would be:

1) Translation 1 unit up

2) Rotation of 90 degrees counterclockwise.

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