Question

how will the coordinates of the vertices of △abc compare to the coordinates of the vertices of △abc? in △abc, each y - coordinate will be than in △abc. 2 less 2 greater

Explanation:

Step1: Recall the rule of horizontal translation

When a figure is translated \(h\) units to the left, the \(x -\)coordinate of each point changes. The formula for a translation \(h\) units to the left is \((x,y)\to(x - h,y)\). Here \(h = 2\).

Step2: Analyze the change in coordinates

For a translation of \(\triangle ABC\) \(2\) units to the left to get \(\triangle A'B'C'\), using the rule \((x,y)\to(x - 2,y)\). The \(y -\)coordinate of each vertex remains the same. There is no change in the \(y -\)coordinate value.

Answer:

The \(y -\)coordinate of each vertex of \(\triangle A'B'C'\) is the same as the \(y -\)coordinate of the corresponding vertex of \(\triangle ABC\). (Since the problem is about filling in the blank based on the drop - down, and there is an error in the problem setup as the translation is horizontal and the \(y -\)coordinate should be unchanged. But if we follow the drop - down options strictly, there is a mistake in the question. However, if we assume it's a mis - labeled drop - down (should be \(x -\)coordinate), for a left - ward translation of \(2\) units, the \(x -\)coordinate of each vertex in \(\triangle A'B'C'\) is \(2\) less than in \(\triangle ABC\))