Question

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

Answer 1

D.

Explanation:

I took the test and got it right.

Answer 2

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

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;

`(x,y)\to (x,y-2)`

`\implies (3,4)\to (3,2)`

`\implies (1,1)\to (1,-1)`

`\implies (5,1)\to (5,-1)`

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

`(x,y)\to (x,-y)`

`\implies (3,2)\to R'(2,-3)`

`\implies (1,-1)\to S'(-1,-1)`

`\implies (5,-1)\to T'(-1,-5)`

Therefore the correct choice is D.