Chapter 9.2, Problem 3CYP

(a)

To determine

Describe the translation from A to B in function notation and in words.

Answer to Problem 3CYP

  $A(-3,-1)\to B(-3+3,-1+2)$ .

The point A is translated 3 units to the right and 2 units upward to reach the point B.

Explanation of Solution

Given:

  

A coin is filmed using stop-motion animation so that it appears to move.

Calculation:

Coordinates of points are:

A(-3,-1) and B(0,1)

Let $A(-3,-1)\to B(-3+a,-1+b)=B(0,1)$ be the translation from A to B.

  $\begin{array}{l}(-3+a,-1+b)=(0,1)\\ \Rightarrow -3+a=0,-1+b=\mathrm{1...........}[(x,y)=(p,q)\iff x=p,y=q]\\ \Rightarrow a=3,b=2\end{array}$

So, the translation is $A(-3,-1)\to B(-3+3,-1+2)$ .

The point A is translated 3 units to the right and 2 units upward to reach the point B.

(b)

To determine

Describe the translation from A to C in function notation and in words.

Answer to Problem 3CYP

  $A(-3,-1)\to B(-3+7,-1+3)$ .

The point A is translated 7 units to the right and 3 units upward to reach the point C.

Explanation of Solution

Given:

  

A coin is filmed using stop-motion animation so that it appears to move.

Calculation:

Coordinates of points are:

A(-3,-1) and C(4,2)

Let $A(-3,-1)\to B(-3+a,-1+b)=B(4,2)$ be the translation from A to B.

  $\begin{array}{l}(-3+a,-1+b)=(4,2)\\ \Rightarrow -3+a=4,-1+b=\mathrm{2...........}[(x,y)=(p,q)\iff x=p,y=q]\\ \Rightarrow a=7,b=3\end{array}$

So, the translation is $A(-3,-1)\to B(-3+7,-1+3)$ .

The point A is translated 7 units to the right and 3 units upward to reach the point C.