Question

Question

Use the image to answer the 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 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

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

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

(−4,−2)

Answer 1

To rotate a point 90 degrees clockwise around the origin (0, 0) in the coordinate plane, we use the following transformation:

If the original point is (x, y), then after a 90-degree clockwise rotation, the new coordinates become (y, -x).

Given the point A (2, 4):

1. Identify x and y:

   • x = 2
   • y = 4

2. Apply the transformation:

   • New x-coordinate = y = 4
   • New y-coordinate = -x = -2

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

Therefore, the response is:

(4,−2)