Question

a polygon has vertices a(6,7), b(8,4), c(5,2), and d(2,3). it was translated by the vector <-4,-2>. what are the new vertices?

Explanation:

Step1: Translate point A

For point \(A(6,7)\), subtract \(4\) from the \(x\)-coordinate and \(2\) from the \(y\)-coordinate.
\(x = 6+( - 4)=2\), \(y = 7+( - 2)=5\), so \(A'(2,5)\)

Step2: Translate point B

For point \(B(8,4)\), \(x = 8+( - 4)=4\), \(y = 4+( - 2)=2\), so \(B'(4,2)\)

Step3: Translate point C

For point \(C(5,2)\), \(x = 5+( - 4)=1\), \(y = 2+( - 2)=0\), so \(C'(1,0)\)

Step4: Translate point D

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

Answer:

The new vertices are \(A'(2,5)\), \(B'(4,2)\), \(C'(1,0)\), and \(D'(-2,1)\)