Answer:
The triangle is reflected across the x-axis and then translated 1 unite to the right , 1 unit up
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
then the new point = (x , -y)
- If point (x , y) reflected across the y-axis
then the new point = (-x , y)
- If the point (x , y) translated horizontally to the right by h units
then the new point = (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then the new point = (x - h , y)
- If the point (x , y) translated vertically up by k units
then the new point = (x , y + k)
- If the point (x , y) translated vertically down by k units
then the new point = (x , y - k)
* Now lets solve the problem
- A triangle has three vertices
- The vertices are B (-3 , 0) , C(2 , -1) , D (-1 , 2)
- The images of the vertices are B" (-2 , 1) , C" (3 , 2) , D" (0 , -1)
after two steps of transformations
- After comparing the points with their images we find
# The x-coordinates of the points are added by 1
∴ There is translation to the right
# The y-coordinates of the points not add or subtracted by the same
number, that means there is a transformation before the translation
for the y-coordinates
# The sign of y-coordinates of the points are changed , that means
there is a reflection across the x-axis
∴ B' is (-3 , 0) , C' is (2 , 1) , D' is (-1 , -2)
- After comparing the 1st image with the 2nd images we find
# The x-coordinates of the points are added by 1 and the
y-coordinates are add by 1
∴ B" is (-2 , 1) , C" is (3 , 2) , D" is (0 , -1)
- From all above
* The triangle is reflected across the x-axis and then translated 1 unite
to the right , 1 unit up
