Answer:
1. Translation 5 units to the left and 1 unit down
2. Reflection across the x-axis
Step-by-step explanation:
Triangle XYZ has its vertices at points X(-6,2), Y(-4,7) and Z(-2,2).
1. Translate triangle XYZ 5 units to the left and 1 unit down. This translation has the rule:
[tex](x,y)\rightarrow (x-5,y-1)[/tex]
Then
[tex]X(-6,2)\rightarrow X'(-11,1);[/tex]
[tex]Y(-4,7)\rightarrow Y'(-9,6);[/tex]
[tex]Z(-2,2)\rightarrow Z'(-7,1).[/tex]
2. Reflect triangle X'Y'Z' across the x-axis. This reflection has the rule:
[tex](x,y)\rightarrow (x,-y)[/tex]
Then
[tex]X'(-11,1)\rightarrow X''(-11,-1);[/tex]
[tex]Y'(-9,6)\rightarrow Y''(-9,-6);[/tex]
[tex]Z'(-7,1)\rightarrow Z''(-7,-1)[/tex]
These points are exactly the vertices of the triangle X''Y''Z''.
