To find the coordinates of X'Y'Z' after rotating triangle XYZ 90° counterclockwise about the origin, we can use the following steps:
Identify the coordinates of each vertex of triangle XYZ.
Apply the 90° counterclockwise rotation rule, which states that when rotating a point 90° counterclockwise about the origin, the new coordinates of the point will be (-y, x).
Substitute the coordinates of each vertex into the rotation rule to find the coordinates of the corresponding vertex in X'Y'Z'.
For example, let's say that the coordinates of triangle XYZ are:
X = (2, 3)
Y = (-1, 4)
Z = (0, -2)
To find the coordinates of X'Y'Z', we can apply the rotation rule to each vertex as follows:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Therefore, the coordinates of X'Y'Z' after rotating triangle XYZ 90° counterclockwise about the origin are:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Note that the order of the vertices may change after the rotation, but the coordinates of each vertex will correspond to the same vertex in the original triangle.