Question

fill in the blank 45 points
given △abc with points a(-2, 3), b(1, 0), and c(-3, 1), graph it, and its image when translated as indicated. then fill in the points for △abc in the space provided.
dado △abc con los puntos a(-2, 3), b(1, 0) y c(-3, 1); graficarlo, y su imagen cuando se traduce como se indica. a continuación, rellene los puntos para △abc en el espacio proporcionado.
⟨-1, 3⟩
answer
a ( type your answer... , type your answer... )
b ( type your answer... , type your answer... )
c ( type your answer... , type your answer... )

Explanation:

Step1: Recall translation rule

To translate a point \((x,y)\) by a vector \(\langle h,k
angle\), the new point is \((x + h, y + k)\). Here, the translation vector is \(\langle -1, 3
angle\), so \(h=-1\) and \(k = 3\).

Step2: Translate point A

For point \(A(-2,3)\), apply the translation: \(x=-2+(-1)=-3\), \(y = 3 + 3=6\). So \(A'(-3,6)\).

Step3: Translate point B

For point \(B(1,0)\), apply the translation: \(x=1+(-1)=0\), \(y = 0+3 = 3\). So \(B'(0,3)\).

Step4: Translate point C

For point \(C(-3,1)\), apply the translation: \(x=-3+(-1)=-4\), \(y = 1+3 = 4\). So \(C'(-4,4)\).

Answer:

\(A'(-3, 6)\)
\(B'(0, 3)\)
\(C'(-4, 4)\)