"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 6 right parenthesis, B left parenthesis 6 comma 4 right parenthesis, and C left parenthesis 2 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 6 comma 2 right parenthesis, B prime left parenthesis negative 4 comma 6 right parenthesis, and C prime left parenthesis negative 2 comma 2 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 6 right parenthesis, B double prime left parenthesis negative 6 comma negative 4 right parenthesis, and C double prime left parenthesis negative 2 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 6 comma negative 2 right parenthesis, B triple prime left parenthesis 4 comma negative 6 right parenthesis, and C triple prime left parenthesis 2 comma negative 2 right parenthesis.

Given point A(2, 6) on the triangle, where would the new point on the triangle be after a rotation of 90 degrees clockwise?

asked by adam

2 months ago

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1 answer

To determine the new coordinates of point A(2, 6) after a 90-degree clockwise rotation around the origin in the coordinate plane, we can use the following transformation formula:

For a point \((x, y)\), the coordinates after a 90-degree clockwise rotation will be \((y, -x)\).

Applying this formula to point A(2, 6):

The x-coordinate is 2 and the y-coordinate is 6.

After rotation, the new coordinates will be:

New x-coordinate: \(y = 6\)

New y-coordinate: \(-x = -2\)

Thus, the new coordinates for point A after a 90-degree clockwise rotation will be:

\[ A' = (6, -2) \]

answered by GPT-4o mini

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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 6 right parenthesis, B left parenthesis 6 comma 4 right parenthesis, and C left parenthesis 2 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 6 comma 2 right parenthesis, B prime left parenthesis negative 4 comma 6 right parenthesis, and C prime left parenthesis negative 2 comma 2 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 6 right parenthesis, B double prime left parenthesis negative 6 comma negative 4 right parenthesis, and C double prime left parenthesis negative 2 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 6 comma negative 2 right parenthesis, B triple prime left parenthesis 4 comma negative 6 right parenthesis, and C triple prime left parenthesis 2 comma negative 2 right parenthesis.

Given point A(2, 6) on the triangle, where would the new point on the triangle be after a rotation of 90 degrees clockwise?

1 answer

To determine the new coordinates of point A(2, 6) after a 90-degree clockwise rotation around the origin in the coordinate plane, we can use the following transformation formula:

For a point \((x, y)\), the coordinates after a 90-degree clockwise rotation will be \((y, -x)\).

Applying this formula to point A(2, 6):

The x-coordinate is 2 and the y-coordinate is 6.
After rotation, the new coordinates will be:
- New x-coordinate: \(y = 6\)
- New y-coordinate: \(-x = -2\)

Thus, the new coordinates for point A after a 90-degree clockwise rotation will be:

\[ A' = (6, -2) \]

Ask a New Question or answer this question.

Given point  A(2, 6) on the triangle, where would the new point on the triangle be after a rotation of 90 degrees clockwise?

GPT-4o mini · Answer

To determine the new coordinates of point A(2, 6) after a 90-degree clockwise rotation around the origin in the coordinate plane, we can use the following transformation formula:

For a point \((x, y)\), the coordinates after a 90-degree clockwise rotation will be \((y, -x)\).

Applying this formula to point A(2, 6):

The x-coordinate is 2 and the y-coordinate is 6.
After rotation, the new coordinates will be:
- New x-coordinate: \(y = 6\)
- New y-coordinate: \(-x = -2\)

Thus, the new coordinates for point A after a 90-degree clockwise rotation will be:

\[ A' = (6, -2) \]