Chapter 9, Problem 17SGR

To determine

To draw the dancers’ final position.

Answer to Problem 17SGR

Trapezoid.

Explanation of Solution

Given:

Thefive dancers are positioned as shown below-

  

Dancers B, F and C move along $(0,-2)$ while dancer A move along $(5,-1)$ .

Calculation:

To translate a point along a vector $(a,b)$ add $a$ to the x-coordinate and add $b$ to the y-coordinate.

  $(x,y)\to (x+a,y+b)$

For dancers B, F and C

  $\begin{array}{l}(x,y)\to (x,y-2)\\ B(3,5)\to B\text{'}(3,3)\\ F(4,4)\to F\text{'}(4,2)\\ C(5,5)\to C\text{'}(5,3)\end{array}$

For dancer A

  $\begin{array}{l}(x,y)\to (x+5,y-1)\\ A(1,5)\to A\text{'}(6,4)\end{array}$

D will be as it is before.

So, the final positions of dancers are-