Question

the vertices of △def are d(2,5), e(6,3), and f(4,0). graph △def and its image when you translate △def using the vector ⟨5,−1⟩.

Explanation:

Step1: Translate point \(D\)

To translate a point \((x,y)\) using the vector \(\langle a,b
angle\), we use the rule \((x + a,y + b)\). For point \(D(2,5)\) with \(a = 5\) and \(b=-1\), we have \(x+5=2 + 5=7\) and \(y+( - 1)=5-1 = 4\). So \(D'(7,4)\)

Step2: Translate point \(E\)

For point \(E(6,3)\), using the same translation rule \(x + 5=6+5 = 11\) and \(y+( - 1)=3-1=2\). So \(E'(11,2)\)

Step3: Translate point \(F\)

For point \(F(4,0)\), \(x + 5=4+5 = 9\) and \(y+( - 1)=0-1=-1\). So \(F'(9,-1)\)

Answer:

Plot \(\triangle DEF\) with vertices \(D(2,5)\), \(E(6,3)\), \(F(4,0)\) and its translated image \(\triangle D'E'F'\) with vertices \(D'(7,4)\), \(E'(11,2)\), \(F'(9,-1)\) on the coordinate - plane.