Question

which translation maps △abc onto its image? 3 units down 3 units up 3 units to the right 3 units to the left

Explanation:

Step1: Analyze the x - coordinates

For point \(A(-4,3)\) and \(A'(-1,3)\), the change in \(x\) - coordinate is \(-1-(-4)=3\).
For point \(B(0,4)\) and \(B'(3,4)\), the change in \(x\) - coordinate is \(3 - 0=3\).
For point \(C(-3,1)\) and \(C'(0,1)\), the change in \(x\) - coordinate is \(0-(-3)=3\).
The \(y\) - coordinates of each pair of points (\(A\) and \(A'\), \(B\) and \(B'\), \(C\) and \(C'\)) remain the same (\(y = 3\) for \(A\) and \(A'\), \(y = 4\) for \(B\) and \(B'\), \(y = 1\) for \(C\) and \(C'\)).

Step2: Determine the translation rule

In a coordinate plane, if \((x,y)\to(x + h,y + k)\), when \(k = 0\) (no vertical change) and \(h>0\) (positive change in \(x\) - coordinate), the translation is \(h\) units to the right. Here \(h = 3\) and \(k=0\).

Answer:

3 units to the right.