ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of B after both reflections?A. (-7, -1)B. (-7, 1)C. (7, 1)D. (7, -1)
Accepted Solution
A:
Answer:The correct option is CStep-by-step explanation:From the given figure it is noticed that the coordinates of point B are (-5,-7).If a figure is reflected across x = 1, then[tex](x,y)\rightarrow (1-(x-1),y)[/tex][tex](x,y)\rightarrow (2-x,y)[/tex]So the coordinates of B after reflection across x = 1 are[tex](-5,-7)\rightarrow (2-(-5),-7)[/tex][tex](-5,-7)\rightarrow (7,-7)[/tex]If a figure is reflected across y = -3, then[tex](x,y)\rightarrow (x,-3-(y+3))[/tex][tex](x,y)\rightarrow (x,-6-y)[/tex]So the coordinates of B after reflection across x = 1 followed by reflection across y= -3 are[tex](7,-7)\rightarrow (7,-6-(-7))[/tex][tex](7,-7)\rightarrow (7,1)[/tex]Therefore the coordinates of the reflection image of B after both reflectionsthe are (7,1) and option C is correct.