Question

△def is translated 5 units down to form its image.
how do the coordinates of the vertices of △def compare to the coordinates of the vertices of △def?
in △def, each is the x - coordinate y - coordinate

Explanation:

Step1: Analyze the change in coordinates

For point \(D(-3,3)\) and \(D'(-3,-2)\), \(x\)-coordinate is \(-3\) for both, \(y\)-coordinate changes from \(3\) to \(-2\) (\(3 - 5=-2\)).
For point \(E(-1,4)\) and \(E'(-1,-1)\), \(x\)-coordinate is \(-1\) for both, \(y\)-coordinate changes from \(4\) to \(-1\) (\(4 - 5=-1\)).
For point \(F(2,1)\) and \(F'(2,-4)\), \(x\)-coordinate is \(2\) for both, \(y\)-coordinate changes from \(1\) to \(-4\) (\(1 - 5=-4\)).

Step2: Compare \(x\) and \(y\) coordinates

We observe that \(x\)-coordinates of vertices of \(\triangle D'E'F'\) are same as \(x\)-coordinates of vertices of \(\triangle DEF\). And \(y\)-coordinates of vertices of \(\triangle D'E'F'\) are \(5\) less than \(y\)-coordinates of vertices of \(\triangle DEF\).

Answer:

In \(\triangle D'E'F'\), each \(y -\)coordinate is \(5\) less than the \(y -\)coordinate of the corresponding vertex in \(\triangle DEF\), while the \(x -\)coordinates remain the same.