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.

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 find the coordinates of point A' after rotating point A (4, 1) 90° counterclockwise, we can use the rotation rule for coordinates:

1. The rule for a 90° counterclockwise rotation about the origin is: \[ (x, y) \rightarrow (-y, x) \]

Applying this rule to the coordinates of point A (4, 1):

• Original coordinates: (4, 1)
• After rotation: \[ A' = (-y, x) = (-1, 4) \]

Now we need to identify which point corresponds to the coordinates (-1, 4) in the provided 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 coordinates (-1, 4) match with point G.

Therefore, the point that represents \( A' \) after rotating \( A(4, 1) \) 90° counterclockwise is point G.