Question

write the coordinates of the vertices after a translation 2 units left and 2 units up.

Explanation:

Step1: Recall the translation rule

For a translation \(2\) units left and \(2\) units up, the rule is \((x,y)\to(x - 2,y+2)\).

Step2: Find the original coordinates

Assume the original coordinates: \(Q(1,-4)\), \(R(6,-4)\), \(S(6,0)\), \(T(1,0)\).

Step3: Apply the translation rule to \(Q\)

For \(Q(1,-4)\): \(x=1,y = - 4\).
\(x-2=1 - 2=-1\), \(y + 2=-4 + 2=-2\). So \(Q'(-1,-2)\).

Step4: Apply the translation rule to \(R\)

For \(R(6,-4)\): \(x = 6,y=-4\).
\(x-2=6 - 2 = 4\), \(y + 2=-4+2=-2\). So \(R'(4,-2)\).

Step5: Apply the translation rule to \(S\)

For \(S(6,0)\): \(x = 6,y = 0\).
\(x-2=6 - 2=4\), \(y + 2=0 + 2=2\). So \(S'(4,2)\).

Step6: Apply the translation rule to \(T\)

For \(T(1,0)\): \(x = 1,y = 0\).
\(x-2=1 - 2=-1\), \(y + 2=0 + 2=2\). So \(T'(-1,2)\).

Answer:

\(Q'(-1,-2)\), \(R'(4,-2)\), \(S'(4,2)\), \(T'(-1,2)\)