Question

graph the image of the figure using the transformation

1. translation: 3 units right

12
a (-4,0) b (1,1)
c (0,-2)
a(-4,0)
c(-3,-2)→c(3 + 3,-2)
c(0,-2)
(x,y)→(x + 3,y)
a(-4,0)→a(-4 + 3,0)=a(-1,0)
b(-2,1)→b(-2 + 3,1)=b(1,1)
find the coordinates of the vertices of each figure af

Explanation:

Step1: Understand the translation rule

A translation of 3 units right means for each point \((x,y)\) in the original figure, the new point \((x',y')\) has the rule \(x'=x + 3\) and \(y'=y\).

Step2: Apply the rule to point \(A\)

If \(A(-4,0)\), then \(x=-4\) and \(y = 0\). Using \(x'=x + 3\), we get \(x'=-4+3=-1\) and \(y'=0\). So \(A'(-1,0)\).

Step3: Apply the rule to point \(B\)

If \(B(-2,1)\), then \(x=-2\) and \(y = 1\). Using \(x'=x + 3\), we get \(x'=-2 + 3=1\) and \(y'=1\). So \(B'(1,1)\).

Step4: Apply the rule to point \(C\)

If \(C(-3,-2)\), then \(x=-3\) and \(y=-2\). Using \(x'=x + 3\), we get \(x'=-3+3 = 0\) and \(y'=-2\). So \(C'(0,-2)\).

Answer:

The coordinates of the vertices of the translated image are \(A'(-1,0)\), \(B'(1,1)\) and \(C'(0,-2)\)