Question

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

Explanation:

Step1: Analyze x - coordinates

The x - coordinates of the points in \(\triangle ABC\) change to new x - coordinates in \(\triangle A''B''C''\). If we look at point \(A(-5,2)\) and \(A''(-1, - 2)\), the x - coordinate of \(A\) changes from \(-5\) to \(-1\), a change of \(4\) units to the right. In general, for a point \((x,y)\) in \(\triangle ABC\), the x - coordinate in \(\triangle A''B''C''\) is \(x + 4\).

Step2: Analyze y - coordinates

The y - coordinates of the points in \(\triangle ABC\) are reflected across the x - axis. For example, point \(B(-2,4)\) has its y - coordinate change from \(4\) to \(-4\) in \(B''(2,-4)\). The transformation for the y - coordinate is \(y
ightarrow - y\).

Answer:

\((x,y)
ightarrow(x + 4,-y)\)