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) graph △abc and △abc on the graph above and to the right
b) give the coordinates of d, e, f, and g after the translation described in part a).

Explanation:

Step1: Find the translation rule

The original coordinate of \(E\) is \((5,-2)\). We want to move \(E\) to the origin \((0,0)\).
Let the translation rule be \((x,y)\to(x + a,y + b)\).
For point \(E\):

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Solve the first equation \(5+a=0\), we get \(a=-5\).
Solve the second equation \(-2 + b=0\), we get \(b = 2\).
So the translation rule is \((x,y)\to(x-5,y + 2)\)

Step2: Apply the translation rule to other points

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

Answer:

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