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 4 comma negative 2 right parenthesis

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

(−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

Answer 1

To rotate a point counterclockwise by 90 degrees, you can use the transformation:

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

Given the point \( A(2, 4) \):

1. Substitute \( x = 2 \) and \( y = 4 \) into the transformation: \[ (2, 4) \rightarrow (-4, 2) \]

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

The correct answer is: (−4, 2).