Question

write the coordinates of the vertices after a translation 2 units left and 2 units up.
$q(,,,,,,,,,,,,)$
$r(,,,,,,,,,,,,)$
$s(,,,,,,,,,,,,)$
$t(,,,,,,,,,,,,)$

Explanation:

Step1: Find the original coordinates

The original coordinates are \(Q(1,-3)\), \(R(5,-3)\), \(S(5,0)\), \(T(1,0)\).

Step2: Apply the translation rule

The translation rule for moving 2 units left (subtract 2 from the \(x\) - coordinate) and 2 units up (add 2 to the \(y\) - coordinate) is \((x,y)\to(x - 2,y + 2)\).
For point \(Q\):
\(x=1-2=-1\), \(y=-3 + 2=-1\), so \(Q'(-1,-1)\)
For point \(R\):
\(x=5-2 = 3\), \(y=-3+2=-1\), so \(R'(3,-1)\)
For point \(S\):
\(x=5-2=3\), \(y=0 + 2=2\), so \(S'(3,2)\)
For point \(T\):
\(x=1-2=-1\), \(y=0+2=2\), so \(T'(-1,2)\)

Answer:

\(Q'(-1,-1)\), \(R'(3,-1)\), \(S'(3,2)\), \(T'(-1,2)\)