Question

1) List the vertices of triangle ABC2) List the vertices of triangle A',B',C', the image of triangle ABC after a rotation of 90 degrees.3) List the vertices of triangle A",B",C", the image of triangle ABC after a rotation of 180 degrees.4) List the vertices of of triangle A"',B"',C"', the image of triangle ABC after a rotation of 270 degrees.

Answer 1

For the first question, you can see in the graph that the triangle ABC has the coordinates

`\begin{gathered} A\colon(1,2) \\ B\colon(2,4) \\ C\colon(4,2) \end{gathered}`

For the second question, you know that if the starting point has coordinates (x,y), a rotation of 90 degrees will have the coordinates (-y,x). So, the vertices of triangle A',B',C', the coordinates of triangle ABC after a rotation of 90 degrees will be

`\begin{gathered} A\colon(1,2)\rightarrow A^(\prime)\colon(-2,1) \\ B\colon(2,4)\rightarrow B^(\prime)\colon(-4,2) \\ C\colon(4,2)\rightarrow C^(\prime)\colon(-2,4) \end{gathered}`

For the third question, you know that if the starting point has coordinates (x,y), a rotation of 180 degrees will have the coordinates (-x,-y). So, the vertices of triangle A'',B'',C'', the coordinates of triangle ABC after a rotation of 180 degrees will be

`\begin{gathered} A\colon(1,2)\rightarrow A^(\doubleprime)\colon(-1,-2) \\ B\colon(2,4)\rightarrow B^(\doubleprime)\colon(-2,-4) \\ C\colon(4,2)\rightarrow C^(\doubleprime)\colon(-4,-2) \end{gathered}`

Finally, for the fourth question, you know that if the starting point has coordinates (x,y), a rotation of 270 degrees will have the coordinates (y,-x). So, the vertices of triangle A''',B''',C''', the coordinates of triangle ABC after a rotation of 270 degrees will be

`\begin{gathered} A\colon(1,2)\rightarrow A^{\doubleprime^(\prime)}^{}\colon(2,-1) \\ B\colon(2,4)\rightarrow B^{\doubleprime^(\prime)}\colon(4,-2) \\ C\colon(4,2)\rightarrow C^{\doubleprime^(\prime)}\colon(2,-4) \end{gathered}`