Use the image to answer the question.

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
?

(1 point)

Answer 1

To determine the point that represents \( A' \) after rotating point \( A(4, 1) \) 90° counterclockwise about the origin, we apply the rotation transformation.

The general rule for rotating a point \( (x, y) \) 90° counterclockwise is: \[ (x, y) \to (-y, x) \]

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

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

We substitute into the transformation: \[ (4, 1) \to (-1, 4) \]

The coordinates \( A' \) after the rotation are \( (-1, 4) \).

Now we need to find which point corresponds to these coordinates from the listed 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)

The point that matches \( (-1, 4) \) is point G.

Thus, the answer is \( G \).