Question

write the coordinates of the vertices after a translation 3 units left and 5 units down.

Explanation:

Step1: Determine the translation rule

For a translation \(3\) units left, we subtract \(3\) from the \(x -\)coordinate. For a translation \(5\) units down, we subtract \(5\) from the \(y -\)coordinate. The rule is \((x,y)\to(x - 3,y - 5)\)

Step2: Find the coordinates of \(D\)

The coordinates of \(D\) are \((1,-3)\).
Using the rule:
\(x=1-3=-2\), \(y=-3 - 5=-8\)
So \(D'(-2,-8)\)

Step3: Find the coordinates of \(E\)

The coordinates of \(E\) are \((1,4)\).
Using the rule:
\(x = 1-3=-2\), \(y=4 - 5=-1\)
So \(E'(-2,-1)\)

Step4: Find the coordinates of \(F\)

The coordinates of \(F\) are \((8,4)\).
Using the rule:
\(x=8 - 3=5\), \(y=4 - 5=-1\)
So \(F'(5,-1)\)

Step5: Find the coordinates of \(G\)

The coordinates of \(G\) are \((8,-3)\).
Using the rule:
\(x=8 - 3=5\), \(y=-3 - 5=-8\)
So \(G'(5,-8)\)

Answer:

\(D'(-2,-8)\), \(E'(-2,-1)\), \(F'(5,-1)\), \(G'(5,-8)\)