Question

triangle def has coordinates ( d(4,-1) ), ( e(5,2) ), and ( f(1,2) ). determine the coordinates of the vertices of the image after a translation along the vector ( (-3,1) ).

a) ( d(-4,1) ), ( e(-5,-2) ), and ( f(-1,-2) )
b) ( d(1,0) ), ( e(2,3) ), and ( f(-2,3) )
c) ( d(5,-1) ), ( e(6,2) ), and ( f(2,2) )
d) ( d(-4,-1) ), ( e(-5,2) ), and ( f(-1,2) )

Explanation:

Step1: Understand the translation vector

A translation vector \((-3,1)\) means subtract \(3\) from the \(x\) - coordinate and add \(1\) to the \(y\) - coordinate of each point.
For point \(D(4,-1)\):
\(x\) - new \(=4+( - 3)=1\), \(y\) - new \(=-1 + 1=0\), so \(D'\) has coordinates \((1,0)\)

Step2: Apply translation to point \(E\)

For point \(E(5,2)\):
\(x\) - new \(=5+( - 3)=2\), \(y\) - new \(=2 + 1=3\), so \(E'\) has coordinates \((2,3)\)

Step3: Apply translation to point \(F\)

For point \(F(1,2)\):
\(x\) - new \(=1+( - 3)=-2\), \(y\) - new \(=2 + 1=3\), so \(F'\) has coordinates \((-2,3)\)

Answer:

B. \(D'(1,0)\), \(E'(2,3)\), and \(F'(-2,3)\)