I need Geometry help

AAA

AAA

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Hi,

Can anyone help me with my high school geometry course. I am taking it online and I want to know how to rotate shapes. I attached an example question. An urgent response please. I am getting behind on this and I have to move on.
 

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Thank you for replying. Can you explain it to me?
 
AAA said:
Can anyone help me with my high school geometry course. I am taking it online and I want to know how to rotate shapes. I attached an example question. An urgent response please. I am getting behind on this and I have to move on.
Click to expand...
What is your understanding of a rotation? How did you get the wrong answers you show? The more you tell us about your own thinking, the better we can help you think correctly.

The hint skeeter gave is that he rotated your entire image, to show that the new location of ABCD looks just like the location of A'B'C'D' in the problem. So the rotation he did is the answer.

To do such a rotation, you can imagine putting a pin at the origin into your desk, and spinning the entire page around it by some angle. Through what angle does point A turn to get to point A'? That is, what is angle AOA'?

Here is some information about rotations:

Geometry Rotation

www.mathsisfun.com

Rotation - MathBitsNotebook(Geo)

mathbitsnotebook.com
 
Hi Dr.Peterson

My understanding of a rotation is when you turn a figure to a fixed point. Like for instance you turn a figure round and round 90 degrees clockwise or something like that. Right? The problem is I don't know how to determine the angle of the rotation. Is there like a formula or something that might help?

Thank you for the sites you provided. They were really helpful. Again thank you so much Dr.Peterson for your help.
 
You ARE TOLD that this is a rotation about the origin. Draw a line from say C to the origin. What is the equation describing that line?
Draw a line from C' to the origin. What is the equation of that line?

Do you notice anything about those two equations?

What does that tell you about the angle that the lines make at the origin?
 
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AAA said:
My understanding of a rotation is when you turn a figure to a fixed point. Like for instance you turn a figure round and round 90 degrees clockwise or something like that. Right? The problem is I don't know how to determine the angle of the rotation. Is there like a formula or something that might help?
Click to expand...
There are trigonometric formulas you could use, but you don't need a formula here. (I don't know whether you have learned anything about general rotations, but as far as I can tell, you probably are doing only "special angles" (like 90, 180, 270 degrees) for which it is easy -- as in the second page I referred you to.

Apart from just drawing in lines from the origin to any one point and its image and seeing visually what the angle is, I would look at the slopes of those two lines. There are simple ways that you have probably learned to tell whether two lines are parallel or perpendicular based on their slopes, and that is all you need. (These are related to the formulas given in the MathBitsNotebook page, which show how to rotate a point about the origin for those special angles -- so you could just write the coordinates of the pair of points and compare them to each formula.)
 
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Draw a line from A to A', from B to B', C to C' and from D to D'. All these lines cross the origin! This tell you that there was a rotation of how many degrees through the origin? Once you get your answer you should study what I wrote.
 
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I get it now. However I have another question.
 
In the problem I attached they tell me that the Point Q was rotated about the origin (0,0) by -45, degrees. What is the of the image of Q, they ask me.Screen Shot 2020-12-03 at 11.53.52 AM.pngScreen Shot 2020-12-03 at 12.01.05 PM.png

This is the explanation they gave me and I don't quite understand it. The area were they say "we want to find the point that would lie on that circle 45 degrees clockwise" is what I don't get. How do I find the angle measure of 45 degrees in the circle?
 
AAA said:
In the problem I attached they tell me that the Point Q was rotated about the origin (0,0) by -45, degrees. What is the of the image of Q, they ask me.View attachment 23461View attachment 23462

This is the explanation they gave me and I don't quite understand it. The area were they say "we want to find the point that would lie on that circle 45 degrees clockwise" is what I don't get. How do I find the angle measure of 45 degrees in the circle?
Click to expand...
If I call the origin O - then rotate the line OQ (-45o), I get point B.
 
AAA said:
In the problem I attached they tell me that the Point Q was rotated about the origin (0,0) by -45, degrees. What is the of the image of Q, they ask me.View attachment 23461View attachment 23462

This is the explanation they gave me and I don't quite understand it. The area were they say "we want to find the point that would lie on that circle 45 degrees clockwise" is what I don't get. How do I find the angle measure of 45 degrees in the circle?
Click to expand...

First, angles are considered to be positive when they rotate counterclockwise, and negative when they rotate clockwise. This is a standard convention.

Second, you can measure the angle with a protractor, or make a 45 degree angle by folding a piece of paper to make a 90 degree angle, then folding in half again. Then compare this to each point.
 
Dr.Peterson said:
First, angles are considered to be positive when they rotate counterclockwise, and negative when they rotate clockwise. This is a standard convention.

Second, you can measure the angle with a protractor, or make a 45 degree angle by folding a piece of paper to make a 90 degree angle, then folding in half again. Then compare this to each point.
Click to expand...

HI Dr. Peterson,

If I measure the angle with a protector how would I know where 45 degrees is? Is there a simpler way to know each angle measurement?
 
AAA said:
I don't see line OQ at all in the graph and I still don't get it because how do I know where -45 degrees is on the graph?
Click to expand...
We said to call the origin "O". The line OQ is the leftmost of the two blue lines. The angle is measured between those blue lines.

AAA said:
If I measure the angle with a protector how would I know where 45 degrees is? Is there a simpler way to know each angle measurement?
Click to expand...
Are you saying you haven't learned how to read the markings on a protractor, or something else?
 
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