Question

Given point A (2, 4) on the triangle in Quadrant I, where is the new point if the triangle is rotated 90 degrees counterclockwise? (1 point)

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

Answer 1

To find the new point after rotating point A (2, 4) by 90 degrees counterclockwise, we can use the following transformation formula:

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

Applying this transformation to point A (2, 4):

1. Calculate the new x-coordinate:
\[
x' = -y = -4
\]

2. Calculate the new y-coordinate:
\[
y' = x = 2
\]

Thus, the rotated point is (-4, 2).

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