Question

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 1

A = (-4,2)
A' = (-2,-3)
A'' = (3,1)
I hope this helps.

Answer 2

The coordinates of vertex A″ are (3,1).

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).