Question

A coordinate plane with 4 quadrants ranges from negative 7 to 7 in unit increments on both the x and y axes. Eight points are plotted and labeled from upper A to upper H. The plotted points are as follows: In quadrant 1, point upper H is shown at 1 increment on the x-axis and 4 increments on the y-axis. Point upper A is shown at 4 increments on the x-axis and 1 increment on the y-axis. In quadrant 2, point upper G is shown at negative 1 increment on the x-axis and 4 increments on the y-axis. Point upper F is shown at negative 4 increments on the x-axis and 1 increment on the y-axis. In quadrant 3, point upper E is shown at negative 4 increments on the x-axis and negative 1 increment on the y-axis. Point upper D is shown at negative 1 increment on the x-axis and negative 4 increments on the y-axis. In quadrant 4, point upper C is shown at 1 increment on the x-axis and negative 4 increments on the y-axis. Point upper B is shown at 4 points on the x-axis and negative 1 increment on the y-axis.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

Pick again its not G

Answer 2

To find the coordinates of point A' after rotating point A(4, 1) 90° counterclockwise around the origin, we can use the rotation formula.

The formula for a 90° counterclockwise rotation of a point (x, y) is given by:

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

Applying this formula to point A(4, 1):

1. Identify \( x = 4 \) and \( y = 1 \).
2. Plug these values into the formula:

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

Thus, the coordinates of point A' after the rotation are (-1, 4).

Now we can match this result with the given points:

- Point H: (1, 4)
- Point A: (4, 1)
- Point G: (-1, 4)
- Point F: (-4, 1)
- Point E: (-4, -1)
- Point D: (-1, -4)
- Point C: (1, -4)
- Point B: (4, -1)

From the list above, we can see that point G is at (-1, 4), which corresponds to A' after the rotation.

Therefore, the answer is:

**G**