Question

the table shows the coordinates of the vertices of \\( \triangle abc \\) and its image. which translation maps \\( \triangle 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 - coordinate change

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 \(0-(-3)=3\).

Step2: Analyze the y - coordinate change

The \(y\) - coordinate of \(A\) and \(A'\) is \(3\), the \(y\) - coordinate of \(B\) and \(B'\) is \(4\), and the \(y\) - coordinate of \(C\) and \(C'\) is \(1\). So, \(y\) - coordinate remains the same.

Since the \(x\) - coordinate of each vertex of \(\triangle ABC\) is increased by \(3\) and \(y\) - coordinate remains unchanged, the translation is \(3\) units to the right.

Answer:

3 units to the right.