Triangle XYZ is the pre-image with vertex X(-6,-4). Given the algebraic rule for the composition,t(3,5) R(270 ,cc) , what are the coordinates of X’?
after translation
... [(-6 + 3),(-4 + 5)] = (-3,1)
after rotation
... (1,3)
(-1,11)
-1,11
To find the coordinates of X', we need to apply the given algebraic rule for the composition of transformations, t(3,5) R(270 ,cc), to the pre-image vertex X(-6,-4).
Let's break down the given rule:
1. t(3,5): This represents a translation by 3 units in the positive x-direction and 5 units in the positive y-direction.
2. R(270 ,cc): This represents a rotation of 270 degrees counterclockwise.
Now, let's apply these transformations step by step:
1. Translation: Add the translation values (3,5) to the pre-image coordinates (-6, -4):
X' = (-6 + 3, -4 + 5) = (-3, 1)
2. Rotation: Rotate the translated point (-3, 1) counterclockwise by 270 degrees around the origin:
The rotation of (x, y) counterclockwise by 270 degrees is (-y, x).
X' = (1, -(-3)) = (1, 3)
Therefore, the coordinates of X' are (1, 3).