Question

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)

Answer 1

The correct option is C

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

`(x,y)\rightarrow (1-(x-1),y)`

`(x,y)\rightarrow (2-x,y)`

So the coordinates of B after reflection across x = 1 are

`(-5,-7)\rightarrow (2-(-5),-7)`

`(-5,-7)\rightarrow (7,-7)`

If a figure is reflected across y = -3, then

`(x,y)\rightarrow (x,-3-(y+3))`

`(x,y)\rightarrow (x,-6-y)`

So the coordinates of B after reflection across x = 1 followed by reflection across y= -3 are

`(7,-7)\rightarrow (7,-6-(-7))`

`(7,-7)\rightarrow (7,1)`

Therefore the coordinates of the reflection image of B after both reflectionsthe are (7,1) and option C is correct.