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What set of transformations is performed on triangle RST to form triangle R’S’T’?

A. A 90-degree counterclockwise rotation about the origin followed by a translation 2 units left
B. A 270-degree counterclockwise rotation about the origin followed by a translation 2 units to the right
C. A translation 2 units down followed by a 90-degree counterclockwise rotation about the origin
D. A translation 2 units down followed by a 270-degree counterclockwise rotation about the origin

What set of transformations is performed on triangle RST to form triangle RST A A 90degree counterclockwise rotation about the origin followed by a translation class=

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Answer:

D. A translation 2 units down followed by a 270-degree counterclockwise rotation about the origin

Step-by-step explanation:

The given triangle has vertices at R(3,4), S(1,1), and T(5,1)

Translating the the vertices down by 2 units, we apply the rule;

[tex](x,y)\to (x,y-2)[/tex]

[tex]\implies (3,4)\to (3,2)[/tex]

[tex]\implies (1,1)\to (1,-1)[/tex]

[tex]\implies (5,1)\to (5,-1)[/tex]

Rotating the resulting vertices through an angle 270 degrees counterclockwise, we apply the rule:

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

[tex]\implies (3,2)\to R'(2,-3)[/tex]

[tex]\implies (1,-1)\to S'(-1,-1)[/tex]

[tex]\implies (5,-1)\to T'(-1,-5)[/tex]

Therefore the correct choice is D.

Answer:

D.

Step-by-step explanation:

I took the test and got it right.

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