Question

1. the coordinates of defg are d(2, -1), e(5, -2), f(4, -5), and g(1, -4).

a) describe in coordinate mapping notation a translation that will move vertex e to the origin.
(x, y) → (__, __)
b) give the coordinates of d, e, f, and g after the translation described in part a).

Explanation:

Step1: Find the translation rule

We want to move \(E(5,-2)\) to \(E'(0,0)\).
The \(x -\)coordinate of \(E\) is \(5\) and we want it to be \(0\), so the change in \(x\) is \(0 - 5=-5\).
The \(y -\)coordinate of \(E\) is \(-2\) and we want it to be \(0\), so the change in \(y\) is \(0-(-2) = 2\).
The translation rule in coordinate - mapping notation is \((x,y)\to(x - 5,y + 2)\)

Step2: Apply the translation rule to other points

For point \(D(2,-1)\):
The \(x -\)coordinate of \(D'\) is \(x=2-5=-3\), the \(y -\)coordinate of \(D'\) is \(y=-1 + 2=1\), so \(D'(-3,1)\)
For point \(F(4,-5)\):
The \(x -\)coordinate of \(F'\) is \(x = 4-5=-1\), the \(y -\)coordinate of \(F'\) is \(y=-5 + 2=-3\), so \(F'(-1,-3)\)
For point \(G(1,-4)\):
The \(x -\)coordinate of \(G'\) is \(x=1-5=-4\), the \(y -\)coordinate of \(G'\) is \(y=-4 + 2=-2\), so \(G'(-4,-2)\)

Answer:

a) \((x,y)\to(x - 5,y + 2)\)
b) \(D'(-3,1)\), \(E'(0,0)\), \(F'(-1,-3)\), \(G'(-4,-2)\)