Question

1. write the transformation needed to go from the original shape to th translations, indicate the up/down & left/right distance. for reflec of reflection. for rotations, indicate how far it rotates.

Explanation:

Step1: Analyze the first pair of shapes (left - hand side)

Observe the positions of corresponding vertices. For example, if we consider a point - by - point comparison. The original shape \(IJHG\) and the transformed shape \(I'J'G'H'\). We can see that if we take a vertex (say \(G\)) and its image \(G'\). The \(y\) - coordinate of \(G\) is negative and the \(y\) - coordinate of \(G'\) is positive. The \(x\) - coordinate of \(G\) and \(G'\) is the same. The line of reflection is the \(x\) - axis. When we reflect a point \((x,y)\) over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\). For all the vertices of the polygon \(IJHG\), reflecting over the \(x\) - axis gives the polygon \(I'J'G'H'\).

Step2: Analyze the second pair of shapes (right - hand side)

Look at the vertices \(TUV\) and \(T'U'V'\). Consider the vertical positions of \(U\) and \(U'\). The \(y\) - coordinate of \(U\) is positive and the \(y\) - coordinate of \(U'\) is negative. The \(x\) - coordinate of \(U\) and \(U'\) is the same. The transformation rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\). For all the vertices of the triangle \(TUV\), reflecting over the \(x\) - axis gives the triangle \(T'U'V'\).

Answer:

For the left - hand side shapes: Reflect over the \(x\) - axis. For the right - hand side shapes: Reflect over the \(x\) - axis.