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 x - coordinates

For \(J(-3,0)\) and \(J'(-3,-4)\), \(K(0,4)\) and \(K'(0,0)\), \(L(2,3)\) and \(L'(2,-1)\), the x - coordinates remain the same (\(-3=-3\), \(0 = 0\), \(2=2\)). So there is no horizontal translation (no shift to the left/right).

Step2: Analyze the y - coordinates

For \(J\): \(y\) - coordinate changes from \(0\) to \(-4\), \(0-(-4)= - 4\). For \(K\): \(y\) - coordinate changes from \(4\) to \(0\), \(4 - 4=0\). For \(L\): \(y\) - coordinate changes from \(3\) to \(-1\), \(3-4=-1\). The formula for a vertical translation is \((x,y)\to(x,y - k)\), where \(k = 4\). A negative change in the \(y\) - coordinate means a downward shift.

Answer:

4 units down