Question

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which translation maps \\( \triangle j k l \\) 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 formula for vertical translation is \(y\to y + k\). Here, \(0 + k=-4\), so \(k=-4\).
For point \(K(0,4)\) and \(K'(0,0)\), the y - coordinate changes from \(y = 4\) to \(y = 0\). Using the formula \(y\to y + k\), \(4 + k=0\), so \(k=-4\).
For point \(L(2,3)\) and \(L'(2,-1)\), the y - coordinate changes from \(y = 3\) to \(y=-1\). Using the formula \(y\to y + k\), \(3 + k=-1\), so \(k=-4\).

Answer:

4 units down