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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 negative 4 comma negative 2 right parenthesis

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

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

To find the new coordinates of point A (2, 4) after a 270-degree counterclockwise rotation around the origin, we can use the following transformation formula for a 270-degree rotation:

For a point (x, y), the coordinates after a 270-degree rotation are given by: \[ (x', y') = (y, -x) \]

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

  1. Replace x with 2 and y with 4:
    • New x-coordinate: y = 4
    • New y-coordinate: -x = -2

Thus, the new coordinates after the rotation are (4, -2).

Therefore, the answer is: (4, -2) (left parenthesis 4 comma negative 2 right parenthesis)