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. Four triangles are plotted on the graph. The four triangles plotted are triangle A B C, triangle A prime B prime C prime, triangle A double prime B double prime C double prime, and triangle A triple prime B triple prime C triple prime. The triangle A B C has its vertices marked with closed points at A left parenthesis 2 comma 4 right parenthesis, B left parenthesis 6 comma 6 right parenthesis, and C left parenthesis 6 comma 2 right parenthesis. The triangle A prime B prime C prime has its vertices marked with closed points at A prime left parenthesis negative 4 comma 2 right parenthesis, B prime left parenthesis negative 6 comma 6 right parenthesis, and C prime left parenthesis negative 2 comma 6 right parenthesis. The triangle A double prime B double prime C double prime has its vertices marked with closed points at A double prime left parenthesis negative 2 comma negative 4 right parenthesis, B double prime left parenthesis negative 6 comma negative 6 right parenthesis, and C double prime left parenthesis negative 6 comma negative 2 right parenthesis. The triangle A triple prime B triple prime C triple prime has its vertices marked with closed points at A triple prime left parenthesis 4 comma negative 2 right parenthesis, B triple prime left parenthesis 6 comma negative 6 right parenthesis, and C triple prime left parenthesis 2 comma negative 6 right parenthesis.Given point A (2, 4) on the triangle Quadrant I, where is the new point if the triangle is rotated 270 degrees counterclockwise?(1 point)Responses (−2,−4)left parenthesis negative 2 comma negative 4 right parenthesis(4,−2) left parenthesis 4 comma negative 2 right parenthesis(−4,−2) left parenthesis negative 4 comma negative 2 right parenthesis(−4, 2) left parenthesis negative 4 comma 2 right parenthesisSkip to navigation

Answer 1

To find the new point after rotating point A (2, 4) 270 degrees counterclockwise around the origin, we can use the general rule for rotation.

The formula for rotating a point (x, y) 270 degrees counterclockwise is given by:
\[
(x', y') = (y, -x)
\]

Applying this to point A (2, 4):
- x' = y = 4
- y' = -x = -2

So after the rotation, point A maps to (4, -2).

The correct response is:
**(4, −2) (4 comma negative 2)**.