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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

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

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

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

(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis
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Answer 1

To find the new position of point A(2, 4) after a 270-degree counterclockwise rotation around the origin, we can use the rotation transformation rules for the coordinate plane.

For a rotation of 270 degrees counterclockwise, the transformation is given by:

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

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

1. Original point: (2, 4)
2. New coordinates after rotation:
   • x-coordinate becomes the original y-coordinate: 4
   • y-coordinate becomes the negative of the original x-coordinate: -2

So, the new point A' becomes:

\[ (4, -2) \]

Therefore, the correct response is:

(4, -2) left parenthesis 4 comma negative 2 right parenthesis.