△PQR is reflected to form​ ​ △P′Q′R′ ​. The vertices of ​ △PQR ​ are P(1,1) , Q(−1,−2) , and R(4,−2) . The vertices of ​ △P′Q′R′ ​ are P′(−1,1) , Q′(1,−2) , and R′(−4,−2) . Which reflection results in the transformation of ​ △PQR ​ ​​to​ ​ △P′Q′R′ ​​​? reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x

Answer:The △PQR is reflected across the y-axis and option 2 is correct.Step-by-step explanation:1. The reflection across the x-axis is defined as[tex](x,y)\rightarrow (x,-y)[/tex]2. The reflection across the y-axis is defined as[tex](x,y)\rightarrow (-x,y)[/tex]3. The reflection across the y=x is defined as[tex](x,y)\rightarrow (y,x)[/tex]4. The reflection across the y=-x  is defined as[tex](x,y)\rightarrow (-y,-x)[/tex]It is given that the vertices of ​ △PQR ​ are P(1,1) , Q(−1,−2) , and R(4,−2) . The vertices of ​ △P′Q′R′ ​ are P′(−1,1) , Q′(1,−2) , and R′(−4,−2) . The relation between prerimage and image is defined as[tex](x,y)\rightarrow (-x,y)[/tex]Therefore the △PQR is reflected across the y-axis and option 2 is correct.