Question

the rectangle cdef, shown below, is translated 3 units to the right and 2 units down to form the image cdef.
draw
write the coordinates of the vertices of cdef.

Explanation:

Step1: Find the original coordinates

The coordinates of \(C=(1,3)\), \(D=(1, - 4)\), \(E=(-6,-4)\), \(F=(-6,3)\)

Step2: Apply the translation rule

The translation rule is \((x,y)\to(x + 3,y-2)\)
For point \(C\):
\(x=1,y = 3\)
\(x+3=1 + 3=4\), \(y-2=3-2 = 1\)
\(C'=(4,1)\)
For point \(D\):
\(x = 1,y=-4\)
\(x+3=1+3 = 4\), \(y-2=-4-2=-6\)
\(D'=(4,-6)\)
For point \(E\):
\(x=-6,y=-4\)
\(x + 3=-6+3=-3\), \(y-2=-4-2=-6\)
\(E'=(-3,-6)\)
For point \(F\):
\(x=-6,y = 3\)
\(x+3=-6 + 3=-3\), \(y-2=3-2=1\)
\(F'=(-3,1)\)

Answer:

\(C'(4,1)\), \(D'(4,-6)\), \(E'(-3,-6)\), \(F'(-3,1)\)