Question

is translated 5 units down to form its image.
complete the table to show the coordinates of the vertices of △def.
△def △def
d(-3,3) ?
e(-1,4)
f(2,1)

Explanation:

Step1: Determine the translation rule

A translation 5 units down means subtracting 5 from the \(y\)-coordinate of each point while keeping the \(x\)-coordinate the same. The rule is \((x,y)\to(x,y - 5)\).

Step2: Apply the rule to point \(D(-3,3)\)

For \(D(-3,3)\), using the rule \((x,y)\to(x,y - 5)\), we substitute \(x=-3\) and \(y = 3\). Then \(y-5=3 - 5=-2\). So \(D'(-3,-2)\).

Step3: Apply the rule to point \(E(-1,4)\)

For \(E(-1,4)\), substitute \(x=-1\) and \(y = 4\) into the rule \((x,y)\to(x,y - 5)\). Then \(y-5=4 - 5=-1\). So \(E'(-1,-1)\).

Step4: Apply the rule to point \(F(2,1)\)

For \(F(2,1)\), substitute \(x = 2\) and \(y=1\) into the rule \((x,y)\to(x,y - 5)\). Then \(y-5=1 - 5=-4\). So \(F'(2,-4)\).

Answer:

\(\triangle DEF\)	\(\triangle D'E'F'\)
\(E(-1,4)\)	\(E'(-1,-1)\)
\(F(2,1)\)	\(F'(2,-4)\)