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 negative 4 comma negative 2 right parenthesis
(4,−2)
left parenthesis 4 comma negative 2 right parenthesis
(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis
(−4, 2)
1 answer
To find the coordinates of the point A (2, 4) after a 90-degree clockwise rotation about the origin, we can use the rotation transformation formula for 90 degrees clockwise, which is:
\[ (x, y) \rightarrow (y, -x) \]
Applying this to the point A (2, 4):
After rotation:
\[ (2, 4) \rightarrow (4, -2) \]
So the new coordinates of point A after rotating 90 degrees clockwise are (4, -2).
The correct response is:
(4,−2) (left parenthesis 4 comma negative 2 right parenthesis)
