Question

graph \\( \triangle a b c \\) with vertices \\( a ( 2,1 ) , b ( - 1,2 ) \\), and \\( c ( - 2 , - 1 ) \\) and its image after the translation \\( ( x , y ) \
ightarrow ( x - 1 , y - 3 ) \\).

Explanation:

Step1: Apply translation to vertex A

For \(A(2,1)\), using \((x,y)\to(x - 1,y - 3)\)
\(x=2-1 = 1\), \(y=1 - 3=-2\), so \(A'(1,-2)\)

Step2: Apply translation to vertex B

For \(B(-1,2)\), using \((x,y)\to(x - 1,y - 3)\)
\(x=-1-1=-2\), \(y=2 - 3=-1\), so \(B'(-2,-1)\)

Step3: Apply translation to vertex C

For \(C(-2,-1)\), using \((x,y)\to(x - 1,y - 3)\)
\(x=-2-1=-3\), \(y=-1 - 3=-4\), so \(C'(-3,-4)\)

Answer:

The vertices of the image \(\triangle A'B'C'\) are \(A'(1,-2)\), \(B'(-2,-1)\), and \(C'(-3,-4)\)