Triangle ABC is translated 2 units right and 5 units down to form triangle A′B′C′. This triangle is then translated 5 units right and 4 units up to form triangle A″B″C″. If vertex A is at (-4, 2), what are the coordinates of vertex A″?
Answer:
The coordinates of vertex A″ are (3,1).
Step-by-step explanation:
It is given that triangle ABC is translated 2 units right and 5 units down to form triangle A′B′C′. It means
\((x,y)\rightarrow (x+2,y-5)\)
\(A(-4,2)\rightarrow A'(-4+2,2-5)=A'(-2,-3)\)
triangle A'B'C' is translated 5 units right and 4 units up to form triangle A″B″C″. it means
\((x,y)\rightarrow (x+5,y+4)\)
\(A'(-2,-3)\rightarrow A''(-2+5,-3+4)=A''(3,1)\)
Therefore the coordinates of vertex A″ are (3,1).