Chapter 14.6, Problem 10WE

a.

To determine

To find appear to be a translation $SoT$ .

Answer to Problem 10WE

It glides a point $4$ units right and $3$ units up.

Explanation of Solution

Given composite of $S\text{ and }T.$

Calculation:

Draw triangle ABC to show the images of the given point under $SoT$ and $ToS.$

  

Consider the composite of $S\text{ and }T$ . $SoT:\left(x,y\right)\to \left(x+4,y+3\right)$

Thus, It glides a point $4$ units right and $3$ units up.

b.

To determine

To justify both $SoT$ and $ToS$ are equal.

Answer to Problem 10WE

Both $SoT$ and $ToS$ are equal.

Explanation of Solution

Given composite of $S\text{ and }T.$

Calculation:

  $SoT:\left(x,y\right)\to \left(x+4,y+3\right)$

It glides a point $4$ units right and $3$ units up.

Consider the composite of $T\text{ and }S$ .

  $ToS:\left(x,y\right)\to \left(x+4,y+3\right)$

It glides a point $4$ units right and $3$ units up.

Thus, both $SoT$ and $ToS$ are equal.

c.

To determine

To find $SoT:\left(x,y\right)\to \left(?,?\right)$ and $ToS:\left(x,y\right)\to \left(?,?\right).$

Answer to Problem 10WE

It glides a point $4$ units right and $3$ units up.

Explanation of Solution

Given composite of $S\text{ and }T.$

Calculation:

  $SoT:\left(x,y\right)\to \left(x+4,y+3\right).$

It glides a point $4$ units right and $3$ units up.

Consider the composite of $T\text{ and }S$ .

  $ToS:\left(x,y\right)\to \left(x+4,y+3\right).$

It glides a point $4$ units right and $3$ units up.