Given the coordinates of XYZ:
X(-5, -4), Y(2, -2), Z(-3, -6)
Here, triangle XYZ was rotated 270 degrees counterclockwise about the origin to get traingle X'Y'Z'.
Let's answer the following.
• Part A.
Let's determine the coordinates of triangle X'Y'Z'.
Apply the rules of roatation.
After a rotation of 270 degrees counterclockwise, the coordinates (x, y) becomes (y, -x).
Applying the rotation rule, we have the coordinates of X'Y'Z' below:
(x, y) ==> (y, -x)
X(-5, -4) ==> (-4, - -5), ==> X'(-4, 5)
Y(2, -2) ==> (-2, -2) ==> Y'(-2, -2)
Z(-3, -6) ==> (-6, - -3) ==> Z'(-6, 3)
Therefore, the coordinates of traingle X'Y'Z' are:
X'(-4, 5)
Y'(-2, -2)
Z'(-6, 3)
• Part B.
To select the general rule that describes the rotation mapping, apply the rotation rules for 270 degrees counterclockwise rotation.
We have:
(x, y) ==> (y, -x)
Therefore, the general rule that describes the rotation mapping is:
(x, y) ==> (y, -x)
ANSWER:
(a) X'(-4, 5)
Y'(-2, -2)
Z'(-6, 3)
(b) (x, y) ==> (y, -x)