Question

a translation is shown on the grid in which triangle a is the pre - image and triangle b is the image.which rule describes the x - coordinates in the translation?

Explanation:

Step1: Analyze the x - coordinate change

Let's take a point from triangle A. For example, assume a vertex of triangle A has an x - coordinate \(x\). After translation, the corresponding vertex of triangle B has an x - coordinate.
If we observe the horizontal shift. Suppose we consider the left - most point of the right - angle of the triangles.
Let the original x - coordinate (from triangle A) be \(x_1\) and the new x - coordinate (from triangle B) be \(x_2\).
If we assume a point in triangle A has \(x\) - coordinate \(x\), and after translation, the \(x\) - coordinate of the corresponding point in triangle B is \(x+0\).
We can also check by using the formula for translation of a point \((x,y)\) in the coordinate plane. A translation rule for the \(x\) - coordinate is of the form \(x'=x + a\), where \(a\) is the horizontal shift.
If we pick two corresponding points (e.g., the vertices of the right - angle). Let's say a point in triangle A is \((x,y)\) and the corresponding point in triangle B is \((x',y')\). By comparing the \(x\) - values of corresponding points (using the grid), we find that \(x'=x+0\).

Answer:

\(x + 0\)