Q&A for How to Rotate a Shape

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How would I rotate a quadrilateral about a point?

Nitakuar

Community Answer

If the point is the origin, then simply apply above the transformation for each of the vertices. If it is some other point, then shift the coordinate axes parallel to the original so it becomes the origin and, after rotation, revert back to the original coordinates.

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Question

What does "around the origin" mean? Does it mean around point (0,0)?

Community Answer

The origin is around (0,0), the center of the diagram.

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Question

What if the number is negative?

Donagan

Top Answerer

If we assume a positive rotation is counterclockwise (anti-clockwise), a negative rotation would be clockwise (to the right at the top).

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Question

How do I rotate a shape if the number is negative and clockwise?

Community Answer

For example, (-3,-5) you would rotate it and 90 degrees would be (-5,3), 180 would be (-5,-3), and 270 would be (5,-3). Clockwise is a direction, so just follow the way the clock moves.

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Question

How do I rotate a shape 180 degrees?

Community Answer

You can rotate a shape 180 degrees by taking a point (x,y) and converting it to (-x,-y).

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Question

How would I rotate a shape 45 about the origin?

Community Answer

First take one of your points -- for example (a,b) -- and simply switch the placement of the coordinates so it makes (b,-a). Repeat this with all points on the shape.

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Question

How do I rotate a shape 90 degrees?

Ray Town

Community Answer

In the examples shown above, you can rotate around the origin by changing (x,y) or (-x,-y) to (-y,x) or (y,-x).

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Question

Is it the same for anti-clockwise and clockwise when rotating a shape?

Community Answer

The procedures are essentially the same whether you're going anti-clockwise (counterclockwise) or clockwise; only the direction of the rotation differs.

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Question

How do I know if a shape should go clockwise or counterclockwise?

Community Answer

It is often mentioned in the directions, so don't worry. But if anything, look to see if it is negative or positive.

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Question

What if the point of rotation is not on the origin but is instead a set of coordinates?

Community Answer

Just think of it as the origin, and rotate in normally 90 degrees like a quarter. 180 like half, 270 like 3/4, and so on.

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Question

How do I rotate a shape if the points are not precisely on the squares?

Community Answer

If the point is not on the squares, then it is not possible to rotate it, even with a graphing calculator. It wouldn't have any specific point, so that is why you cannot rotate it.

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Question

How do I rotate a number clockwise?

Community Answer

You don't need to. In order to figure out the points for a negative 270-degree question, just use the formula for the 90-degree formula and vice versa and you can just use the same formula for a 180-degree question.

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