Question

the table shows the coordinates of the vertices of △jkl and its image. which translation maps △jkl onto its image? 4 units down 4 units up 4 units to the right 4 units to the left

Explanation:

Step1: Analyze the change in y - coordinates

For point \(J(-3,0)\) and \(J'(-3,-4)\), the y - coordinate changes from \(y = 0\) to \(y=-4\). The change is \(0-(-4)= - 4\).
For point \(K(0,4)\) and \(K'(0,0)\), the y - coordinate changes from \(y = 4\) to \(y = 0\). The change is \(4 - 0=4\) (but in the negative direction).
For point \(L(2,3)\) and \(L'(2,-1)\), the y - coordinate changes from \(y = 3\) to \(y=-1\). The change is \(3-(-1)= - 4\).

Step2: Determine the translation rule

In a translation \((x,y)\to(x,y + k)\), when \(k=-4\), the translation is \(4\) units down. Since the x - coordinates of \(J\), \(K\), and \(L\) remain the same (\(x\) - coordinate of \(J\): \(-3\) vs \(-3\), \(x\) - coordinate of \(K\): \(0\) vs \(0\), \(x\) - coordinate of \(L\): \(2\) vs \(2\)), and the y - coordinate of each point is decreased by \(4\).

Answer:

4 units down