Question

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

Explanation:

Step1: Analyze horizontal movement

The $x$ - coordinates of points in $\triangle ABC$ increase by 4 to get to $\triangle A''B''C''$. For example, the $x$ - coordinate of $A$ is - 5 and of $A''$ is - 1. This indicates a translation of 4 units to the right, which is represented as $(x,y)\to(x + 4,y)$ in the first - part of the transformation.

Step2: Analyze vertical movement and reflection

The $y$ - coordinates of points in $\triangle ABC$ change sign and seem to be reflected over the $x$ - axis. For example, the $y$ - coordinate of $B$ is 4 and of $B''$ is - 4. The transformation for reflection over the $x$ - axis is $(x,y)\to(x,-y)$. Combining the horizontal translation and the reflection over the $x$ - axis, the composition transformation mapping is $(x,y)\to(x + 4,-y)$.

Answer:

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