Question

Point A is the original point before rotating. Which point represents A' after A(4, 1) is rotated 90° counterclockwise: B, C, D, E, F, G, or H?

Answer 1

To determine the coordinates of point A' after rotating point A(4, 1) 90° counterclockwise, you can use the rotation formula for a point (x, y). The new coordinates after a 90° counterclockwise rotation are given by:

\[
(x', y') = (-y, x)
\]

Given point A(4, 1):

1. \(x = 4\)
2. \(y = 1\)

Applying the formula:

\[
x' = -y = -1
\]
\[
y' = x = 4
\]

Thus, the coordinates of point A' after a 90° counterclockwise rotation are:

\[
A'(-1, 4)
\]

Now, you can look for the point (−1, 4) among the options B, C, D, E, F, G, or H. The option that matches this result is the one that represents point A' after the rotation.