We are given the following points
A(-1, 4)
B(1, 2)
C(-2, 1)
We are asked to first reflect the points ABC over the y-axis, then rotate the image 90° counter-clockwise about the origin.
Reflection over the y-axis:
To reflect the points ABC over the y-axis, the rule is
(x, y) = (-x, y)
So we have to reverse the sign of the x-coordinate and leave the y-coordinate as it is.
A(-1, 4) = A'(1, 4)
B(1, 2) = B'(-1, 2)
C(-2, 1) = C'(2, 1)
As you can see, we have reversed the sign of x-coordinate.
Rotation of 90° counter-clockwise:
To rotate the points ABC 90° counter-clockwise about the origin, the rule is
(x, y) = (-y, x)
So we have to shuffle the positions of x and y and also reverse the sign of the y-coordinate.
A'(1, 4) = A'(-4, 1)
B'(-1, 2) = B'(-2, -1)
C'(2, 1) = C'(-1, 2)
Therefore, the coordinates of the final image after both transformation are
A'(-4, 1)
B'(-2, -1)
C'(-1, 2)