Question

identify the sequence of transformations that will carry △abc→△abc. give your answer in the form of a composition transformation mapping. (1 point) o (x,y)→(x, -y - 4) o (x,y)→(x, -y + 4) o (x,y)→(x - 4,-y) o (x,y)→(x + 4,-y)

Explanation:

Step1: Analyze y - coordinate change

When a point \((x,y)\) is transformed, if we consider the general form of transformation for the y - coordinate. Let's assume the original point is \((x,y)\) and the new point is \((x',y')\). We need to find how the y - value changes.

Step2: Check the given options

For a transformation of the form \((x,y)\to(x, - y + k)\), it first reflects the point across the x - axis (changing \(y\) to \(-y\)) and then translates it vertically by \(k\) units. Looking at the problem, we assume a vertical transformation related to the y - coordinate. If we consider the change in the position of the points from \(\triangle ABC\) to \(\triangle A''B''C''\), we note that there is a reflection across the x - axis and a vertical translation. If we start with a point \((x,y)\), reflecting it across the x - axis gives \((x,-y)\) and then translating it down by 4 units gives \((x,-y - 4)\).

Answer:

\((x,y)\to(x,-y - 4)\)