Question

1. determine a series of transformations that would map figure t onto figure u.

Explanation:

Step1: Reflect over the y - axis

When reflecting a point \((x,y)\) over the \(y\) - axis, the transformation rule is \((x,y)\to(-x,y)\). This will flip Figure \(T\) to the right - hand side of the \(y\) - axis.

Step2: Translate up

Count the vertical distance between the corresponding points of the reflected Figure \(T\) (after step 1) and Figure \(U\). Let's assume a general point \((x,y)\) after reflection. If we need to move it up by \(k\) units, the transformation rule is \((x,y)\to(x,y + k)\). By observing the \(y\) - coordinates of corresponding vertices, we can find the value of \(k\). For example, if a vertex of the reflected Figure \(T\) has \(y\) - coordinate \(y_1\) and the corresponding vertex of Figure \(U\) has \(y\) - coordinate \(y_2\), then \(k=y_2 - y_1\).

Answer:

A reflection over the \(y\) - axis followed by a translation up.