Question

how do the coordinates of the vertices of
\\( \triangle d ^ { prime } e ^ { prime } f ^ { prime } \\) compare to the coordinates of
the vertices of \\( \triangle d e f \\)?
in \\( \triangle d ^ { prime } e ^ { prime } f ^ { prime } \\), each ? is
? than in \\( \triangle d e f \\).

Explanation:

Step1: Analyze the x - coordinates

For point \(D(-3,3)\) and \(D'(-3,-2)\), \(x = - 3\) for both. For point \(E(-1,4)\) and \(E'(-1,-1)\), \(x=-1\) for both. For point \(F(2,1)\) and \(F'(2,-4)\), \(x = 2\) for both. So the \(x -\)coordinates remain the same.

Step2: Analyze the y - coordinates

For \(D\): \(y = 3\), for \(D'\): \(y=-2\), \(3-(-2)=5\). For \(E\): \(y = 4\), for \(E'\): \(y=-1\), \(4-(-1)=5\). For \(F\): \(y = 1\), for \(F'\): \(y=-4\), \(1-(-4)=5\). The \(y -\)coordinates of \(\triangle D'E'F'\) are \(5\) less than the \(y -\)coordinates of \(\triangle DEF\)

Answer:

In \(\triangle D'E'F'\), each \(y-\)coordinate is \(5\) less than in \(\triangle DEF\)