Chapter 11.6, Problem 14HP

To determine

Tocalculate : The coordinate of the image after a series of operation..

Answer to Problem 14HP

  $A\text{'}\text{'}\text{'}(-4,5)$ , $B\text{'}\text{'}\text{'}(-1,0)$ and $C\text{'}\text{'}\text{'}(-2,0)$

Explanation of Solution

Given information : The given coordinate are $A(-3,4),B(-2,1)$ and $C(2,2)$

Formula used : The $90°$ clockwise rotation will map point $P(x,y)$ in to $P\text{'}(y,-x)$ . And, after translating $k$ units up the point $P\text{'}(y,-x)$ will become $P\text{'}\text{'}(y,-x+k)$ . Also, after a reflection over the y-axis, the point $P\text{'}\text{'}(y,-x+k)$ will become $P\text{'}\text{'}\text{'}(-y,-x+k)$

Calculation : Plug the $k=2$ in the above formula, will get the point transformed.

  $P(x,y)$ in to $P\text{'}\text{'}\text{'}(-y,-x+k)$

  $A(-3,4)$ in to $A\text{'}\text{'}\text{'}(-4,-(-3)+2)=A\text{'}\text{'}\text{'}(-4,5)$

  $B(-2,1)$ in to $B\text{'}\text{'}\text{'}(-1,-(-2)+2)=B\text{'}\text{'}\text{'}(-1,4)$

  $C(2,2)$ in to $C\text{'}\text{'}\text{'}(-2,-2+2)=C\text{'}\text{'}\text{'}(-2,0)$