Given point A (2, 4)

Question

𝐴

(
2
,

4
)
on the triangle in Quadrant I, where is the new point if the triangle is rotated 90 degrees counterclockwise?

(1 point)
Responses

(−4, 2)
(
−
4
,

2
)
left parenthesis negative 4 comma 2 right parenthesis

(−4,−2)
(
−
4
,
−
2
)
left parenthesis negative 4 comma negative 2 right parenthesis

(4,−2)
(
4
,
−
2
)
left parenthesis 4 comma negative 2 right parenthesis

(−2,−4)

Answer 1

To rotate the point \( A(2, 4) \) 90 degrees counterclockwise around the origin, you can use the transformation formula for rotation:

\[ (x, y) \rightarrow (-y, x) \]

Applying this transformation to the point \( (2, 4) \):

1. Substitute \( x = 2 \) and \( y = 4 \):

\[ (-y, x) = (-4, 2) \]

So the new point after rotating \( A(2, 4) \) 90 degrees counterclockwise is \( (-4, 2) \).

Thus, the correct response is:

(−4, 2)