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.

Question

Given point A (2, 4) on the triangle Quadrant I, where is the new point if the triangle is rotated 270 degrees counterclockwise?

Answer 1

To determine the new coordinates of point A(2, 4) after a 270-degree counterclockwise rotation about the origin, we can use the rotation formula for 270 degrees counterclockwise:

\[ (x', y') = (y, -x) \]

Here, \(x\) is the original x-coordinate and \(y\) is the original y-coordinate.

1. Original point A is (2, 4).
2. Applying the rotation formula:
   • For \(x' = y = 4\)
   • For \(y' = -x = -2\)

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