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 in Quadrant I, how would you describe the coordinates of the new point when the triangle is rotated 90 degrees clockwise?
(1 point)
Responses
(4,−2)
left parenthesis 4 comma negative 2 right parenthesis
(−4, 2)
left parenthesis negative 4 comma 2 right parenthesis
(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis
(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis
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1 answer
To rotate a point 90 degrees clockwise around the origin in the coordinate plane, you can use the following transformation:
If a point has coordinates \((x, y)\), after a 90-degree clockwise rotation, its new coordinates will be \((y, -x)\).
Starting with point \(A(2, 4)\):
Applying the transformation:
Thus, the new coordinates after the rotation are \((4, -2)\).
The correct response is: (4, -2).
