Question

Question

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 8 to 8 in increments of 1. A triangle A B C is plotted on the graph. The triangle A B C has its vertices marked with closed points at A left parenthesis 2 comma 6 right parenthesis, B left parenthesis 6 comma 4 right parenthesis, and C left parenthesis 2 comma 2 right parenthesis.

Given point A(2, 6)
on the triangle, where would the new point on the triangle be after a rotation of 90 degrees counterclockwise?

Answer 1

To determine the new position of point A(2, 6) after a 90-degree counterclockwise rotation around the origin, we can use the following transformation rule for 90-degree counterclockwise rotation:

If a point \( (x, y) \) is rotated 90 degrees counterclockwise around the origin, its new coordinates \( (x', y') \) will be given by: \[ (x', y') = (-y, x) \]

For point A(2, 6):

• Original coordinates: \( (x, y) = (2, 6) \)
• Apply the transformation:
  • \( x' = -y = -6 \)
  • \( y' = x = 2 \)

Thus, after a 90-degree counterclockwise rotation, point A(2, 6) will move to: \[ A'(-6, 2) \]

Therefore, the new point on the triangle after the rotation is at \( A'(-6, 2) \).