Question

part a:
possible points: 3.5
quadrilateral abcd has coordinates ( a(0,2), b(3,4), c(4,2) ), and ( d(3,0) ).
determine the coordinates of the vertices of ( a^{prime}b^{prime}c^{prime}d^{prime} ) after a translation along the vector ( langle-2,3
angle )

Explanation:

Step1: Apply translation rule

The translation vector is \(\langle - 2,3
angle\). For a point \((x,y)\) translated by \(\langle a,b
angle\), the new point is \((x + a,y + b)\). Here \(a=-2\) and \(b = 3\).
For point \(A(0,2)\):
\(x=0,y = 2\). New \(x\) - coordinate \(x'=0+( - 2)=-2\), new \(y\) - coordinate \(y'=2 + 3=5\). So \(A'(-2,5)\)

Step2: Translate point \(B(3,4)\)

\(x = 3,y=4\). New \(x\) - coordinate \(x'=3+( - 2)=1\), new \(y\) - coordinate \(y'=4 + 3=7\). So \(B'(1,7)\)

Step3: Translate point \(C(4,2)\)

\(x = 4,y = 2\). New \(x\) - coordinate \(x'=4+( - 2)=2\), new \(y\) - coordinate \(y'=2+3 = 5\). So \(C'(2,5)\)

Step4: Translate point \(D(3,0)\)

\(x = 3,y = 0\). New \(x\) - coordinate \(x'=3+( - 2)=1\), new \(y\) - coordinate \(y'=0 + 3=3\). So \(D'(1,3)\)

Answer:

\(A'(-2,5),B'(1,7),C'(2,5),D'(1,3)\)