Question

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 \(J(-3,0)\) to \(J'(-3,-4)\), the y - coordinate changes from \(0\) to \(-4\). The formula for vertical translation is \(y
ightarrow y + k\). Here, \(0 + k=-4\), so \(k = - 4\).
For point \(K(0,4)\) to \(K'(0,0)\), the y - coordinate changes from \(4\) to \(0\). Using \(y
ightarrow y + k\), \(4 + k=0\), so \(k=-4\).
For point \(L(2,3)\) to \(L'(2,-1)\), the y - coordinate changes from \(3\) to \(-1\). Using \(y
ightarrow y + k\), \(3 + k=-1\), so \(k = - 4\).

Step2: Determine the direction of translation

Since \(k=-4\), and in the vertical translation formula \(y
ightarrow y + k\), a negative \(k\) value means a downward translation.

Answer:

4 units down