Chapter 14.6, Problem 12WE

a.

To determine

To find $T:M\to ?.$

Answer to Problem 12WE

The value of $T:M\to L.$

Explanation of Solution

Given $L,M\text{ and }N$ are the midpoints of triangle $QRS.$

Calculation:

Now consider a translation that maps point $R$ to the point $N$ and as parallelism is invariant under translation.

Therefore, the translation will map point $M$ to the point $L$ .

Thus, $T:M\to L.$

b.

To determine

To find $To{D}_{S,\frac{1}{2}}:R\to ?.$

Answer to Problem 12WE

The value of $To{D}_{S,\frac{1}{2}}:R\to L.$

Explanation of Solution

Given $L,M\text{ and }N$ are the midpoints of triangle $QRS.$

Calculation:

Under a dilation of scalar factor $\frac{1}{2}$ with respect to the point $S$ the point $R$ will map at the point $M$ and as parallelism is invariant under translation.

Therefore, the translation will map point $M$ to the point $L.$

Thus, $To{D}_{S,\frac{1}{2}}:R\to L.$

c.

To determine

To find $ToT:R\to ?.$ .

Answer to Problem 12WE

The value of $ToT:R\to Q.$

Explanation of Solution

Given $L,M\text{ and }N$ are the midpoints of triangle $QRS.$

Calculation:

The given translation that maps point $R$ to the point $N$ and if the translation is repeated again it will follow the straight line and it will map point $N$ to the point $Q.$

Thus, $ToT:R\to Q.$