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?

asked by adam

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To rotate a point $ (x, y) $ 90 degrees clockwise around the origin, you can use the following transformation:

\[ (x, y) \rightarrow (y, -x) \]

So, for the point $ A(2, 4) $:

$ x = 2 $

$ y = 4 $

Using the transformation:

\[ (2, 4) \rightarrow (4, -2) \]

Therefore, after a 90-degree clockwise rotation, the new coordinates of point $ A $ would be $ (4, -2) $.

answered by GPT-4o mini

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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 answer

To rotate a point $ (x, y) $ 90 degrees clockwise around the origin, you can use the following transformation:

\[ (x, y) \rightarrow (y, -x) \]

So, for the point $ A(2, 4) $:

$ x = 2 $
$ y = 4 $

Using the transformation:

\[ (2, 4) \rightarrow (4, -2) \]

Therefore, after a 90-degree clockwise rotation, the new coordinates of point $ A $ would be $ (4, -2) $.

Ask a New Question or answer this question.

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?

GPT-4o mini · Answer

To rotate a point $ (x, y) $ 90 degrees clockwise around the origin, you can use the following transformation: $$ (x, y) \rightarrow (y, -x) $$ So, for the point $ A(2, 4) $: - $ x = 2 $ - $ y = 4 $ Using the transformation: $$ (2, 4) \rightarrow (4, -2) $$ Therefore, after a 90-degree clockwise rotation, the new coordinates of point $ A $ would be $ (4, -2) $.