We have the following coordinates for the vertices of a quadrilateral:
• A = (1,1)
,
• B = (3,4)
,
• C = (8,3)
,
• D = (4,3)
We must perform the following transformation to the points:
0. A rotation of 180° about the origin.
,
1. A translation of 6 units up.
We make the rotation and then the translation.
1) We must note that the rule for a rotation by 180° about the origin is:
[tex]X=(x,y)\rightarrow X^{\prime}=(-x,-y)[/tex]
Making the rotation to the points, we get:
A' = (-1,-1)
B' = (-3,-4)
C' = (-8,-3)
D' = (-4,-3)
2) The translation of the points in 6 units up consists in making the following transformation:
[tex]X^{}=(x,y)\rightarrow X^{\prime}=(x,y+6)[/tex]
Making the translation, we get:
A'' = (-1,-1 + 6) = (-1,5)
B'' = (-3,-4 + 6) = (-3,2)
C'' = (-8,-3 + 6) = (-8,3)
D'' = (-4,-3 + 6) = (-4,3)
Answer
After making the two transformations to the points their coordinates are:
A'' = (-1,5)
B'' = (-3,2)
C'' = (-8,3)
D'' = (-4,3)
