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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

(−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)

Answer 1

To find the new coordinates of point A (2, 4) after rotating it 270 degrees counterclockwise around the origin, we can use the rotation transformation rules for coordinates.

The rule for a 270-degree counterclockwise rotation is:

• If \( (x, y) \) is the original point, then the new coordinates \( (x', y') \) after rotation will be: \[ (x', y') = (y, -x) \]

Applying this to point A (2, 4):

• \( x = 2 \)
• \( y = 4 \)

Now, substitute these values into the rotation formula: \[ x' = y = 4 \] \[ y' = -x = -2 \]

Thus, the new coordinates of point A after a 270-degree counterclockwise rotation are \( (4, -2) \).

Therefore, the answer is: (4, −2).