Question

warm up
4 units left and 2 units down
write the rule used and write the coordinates of the pre - image and image
$(x,y)=>()$
$p()=>p()$
$q()=>q()$
$r()=>r()$
$s()=>s()$

Explanation:

Step1: Determine the translation rule

When moving 4 units left, we subtract 4 from the \(x -\)coordinate. When moving 2 units down, we subtract 2 from the \(y -\)coordinate. So the rule is \((x,y)\to(x - 4,y - 2)\)

Step2: Find coordinates of \(P\) and \(P'\)

From the graph, \(P=(1,3)\). Using the rule \(x=1-4=-3\), \(y = 3-2 = 1\), so \(P'=(-3,1)\)

Step3: Find coordinates of \(Q\) and \(Q'\)

From the graph, \(Q=(4,4)\). Using the rule \(x=4 - 4=0\), \(y=4 - 2=2\), so \(Q'=(0,2)\)

Step4: Find coordinates of \(R\) and \(R'\)

From the graph, \(R=(5,1)\). Using the rule \(x=5 - 4 = 1\), \(y=1 - 2=-1\), so \(R'=(1,-1)\)

Step5: Find coordinates of \(S\) and \(S'\)

From the graph, \(S=(1,0)\). Using the rule \(x=1 - 4=-3\), \(y=0 - 2=-2\), so \(S'=(-3,-2)\)

Answer:

\((x,y)\Rightarrow(x - 4,y - 2)\)
\(P(1,3)\Rightarrow P'(-3,1)\)
\(Q(4,4)\Rightarrow Q'(0,2)\)
\(R(5,1)\Rightarrow R'(1,-1)\)
\(S(1,0)\Rightarrow S'(-3,-2)\)