Question

the figure below has a point marked with a large dot. first, rotate the figure 90° counterclockwise about the origin. then, give the coordinates of the marked point in the original figure and the final figure. point in original figure: (\square,\square) point in final figure: (\square,\square)

Explanation:

Step1: Find original coordinates

From the grid, the marked point is at \( (2, 4) \) (x=2, y=4).

Step2: Apply 90° counterclockwise rotation

The rule for rotating a point \( (x, y) \) 90° counterclockwise about the origin is \( (x, y) \to (-y, x) \). Substituting \( x = 2 \), \( y = 4 \), we get \( (-4, 2) \).

Answer:

Point in original figure: \( (2, 4) \)
Point in final figure: \( (-4, 2) \)