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The Effects of Transformations on Lines Practice
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Question
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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)

1 answer

To determine which point represents \( A' \) after rotating point \( A(4, 1) \) 90° counterclockwise, we can use the following rule for 90° counterclockwise rotation:

If the original point is \((x, y)\), the new coordinates after rotation will be \((-y, x)\).

So for point \( A(4, 1) \):

  • The \( x \) coordinate is 4 and the \( y \) coordinate is 1.
  • After rotating 90° counterclockwise, the new coordinates will be \((-1, 4)\).

Now we need to locate the point with coordinates \((-1, 4)\) among the given points:

  • Point \( H \) is at \((1, 4)\)
  • Point \( A \) is at \((4, 1)\)
  • Point \( G \) is at \((-1, 4)\) (this matches the rotated coordinates)
  • Point \( F \) is at \((-4, 1)\)
  • Point \( E \) is at \((-4, -1)\)
  • Point \( D \) is at \((-1, -4)\)
  • Point \( C \) is at \((1, -4)\)
  • Point \( B \) is at \((4, -1)\)

Therefore, the point that represents \( A' \) after the rotation is point \( G \) at \((-1, 4)\).

Answer: G