Question

Given point A(2, 6)
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 rotate a point \( A(x, y) \) by 90 degrees counterclockwise around the origin, you can use the following transformation:

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

For the point \( A(2, 6) \):

- \( x = 2 \)
- \( y = 6 \)

Applying the transformation:

\[
x' = -y = -6
\]
\[
y' = x = 2
\]

Thus, the new point after a 90-degree counterclockwise rotation would be:

\[
A'(-6, 2)
\]

Therefore, after a 90-degree counterclockwise rotation, the new point on the triangle is \( A'(-6, 2) \).