Question

write the coordinates of the vertices after a translation 7 units left and 1 unit up.

Explanation:

Step1: Find the original coordinates

The original coordinates are \(E(3,1)\), \(D(5,-3)\), \(C(3,-6)\), \(F(-1,-3)\).

Step2: Apply the translation rule

The translation rule for moving 7 units left (subtract 7 from \(x\)-coordinate) and 1 unit up (add 1 to \(y\)-coordinate) is \((x,y)\to(x - 7,y + 1)\).
For point \(E\):
\(x=3-7=-4\), \(y = 1+1=2\), new coordinate \(E'(-4,2)\)
For point \(D\):
\(x=5-7=-2\), \(y=-3 + 1=-2\), new coordinate \(D'(-2,-2)\)
For point \(C\):
\(x=3-7=-4\), \(y=-6 + 1=-5\), new coordinate \(C'(-4,-5)\)
For point \(F\):
\(x=-1-7=-8\), \(y=-3 + 1=-2\), new coordinate \(F'(-8,-2)\)

Answer:

\(E'(-4,2)\), \(D'(-2,-2)\), \(C'(-4,-5)\), \(F'(-8,-2)\)