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What is a prime and double prime notation on a coordinate plane?
I'm working on a math portfolio and I'm stuck at the prime and double prime notations!
On a coordinate plane, draw a six-sided, closed figure composed of only straight lines that lie in only one quadrant. Label each vertex with a letter from A to F. Identify the coordinates of each vertex. Pick two line segments, name them, and find their slope. Remember a line segment is named using its endpoints. Translate your figure according to the rule (x, y) (x – 4, y + 2). Draw the image in a different color. Identify and label the vertices of the image using prime notation. Using the same line segments used in Step 2, name and find the slope of the two line segments from the translated figure. Reflect the result of the translation over the x axis. Draw the image in a different color. Identify and label the vertices of the image using double prime notation. Using the same line segments used in Step 2 and Step 5, name and find the slope of the two line segments from the reflected figure.
I'm not positive, but I believe when they say prime and double prime notation, they want to rename the vertices after you translate them. Like, your first vertices are labeled A to F. Then you do the translation and rename the new vertices as A', B', C', etc. Once you do the reflection, you name that new set of vertices as A'', B'', C'', etc. I assume thats what it means.
Oh ok. Thanks! I'm not sure how to translate it though.
I'm also not sure how to label the vertices in prime and double prime notations.
Oh ok. So is the prime and double prime notations labeled as ' and "? Prime notation being labeled as ' and double prime notation being labeled as " ?
Well, once you have chosen and names your vertices, figure out what coordinate points those vertices specifically lie at. Then you're given the translation rule (x-4, y+2). All this means is take eachcoordinate point, subtract 4 from the x coordinate and add 2 to the y coordinate. Here is a quick example |dw:1433534371381:dw|
Once I moved the rectangle, I just relabeled each vertex as A', B', C', D'. Then you would perform a reflection and relabel the vertices A'', B'', etc. THats what they want you to do with your example.
I'm trying to attach a photo of what I did so far but it won't seem to work.
Okay, no problem.
Do you know how to attach pictures?
Yep, looks good. Just make sure the vertices for your translated figure in blue are labeled as A', B', etc. Use the apostrophe dash thingy next to them, lol.
Sweet! That's the first 3 steps of the instructions that I posted.
Yep, so just find the slopes of any of the two line segments, reflect the figure, rename the vertices with '' and get the slopes again. Shouldnt be too bad :)
Oh ok. Sweet! Thanks man!! You helped a lot!! If I need anymore help with it I'll let you know! :)
Okay, will do :3
I'm not sure how to draw the double notation figure over the x axis?
Well, if you're reflecting over the x-axis, then you're simply changing the sign of your y-coordinates.
When I calculate the translation for the double prime notation figure the coordinates are still in the upper left quadrant.
The rule is (x-4 , y+2)
They shouldn't be. From your image, you have the coordinates: (-9,17) (-12,14) (-12,11) (-9,8) (-6,11) (-6,14) And that rule was only for the translation. Now you have a reflection, which means flipping your figure symmetricall with respect to some axis. In the case of reflection about the x-axis, this is equivalent to changing the sign of your y-coordinates. So the 6 vertices posted should now all change their y-coordinates to negative. Your next figure after the reflection should have these vertices: (-9,-17) (-12,-14) (-12,-11) (-9,-8) (-6,-11) (-6,-14)
Oh ok. So that will give me the coordinates to allow the double prime notation figure to be drawn over the x axis?
Ok. Sweet! Thanks man!! I'll work on it and if I have anymore questions I'll let you know.
Alright then :)
Here's the same coordinate plane with the double prime notation figure on it. I just put the dots for right now because I don't know if I did it right. It didn't end up being over the x axis so I don't know if I did something wrong. @Concentrationalizing
Is it supposed to be drawn right on top of the x axis or is it talking about drawing it on the other side of the x axis opposite of the prime notation figure?
No, thats over the x-axis, that's perfectly fine. Think of reflection about (or over) the x-axis like this: |dw:1433538132502:dw| Its kind of like as if you spun a fan. If you have a fan blade that, when at the top, is 5 inches away above the rotor where it's rotating and then you spin it to now where its underneath (like a reflection), then the fan blade is now 5 inches away from the rotor below. Everything is reflected to the opposite side and the distance away from the axis is still the same. If that makes any sense.
Oh ok. So it's like looking at your reflection in a mirror and the mirror being the x axis?
Whatever is on top is copied on the other side of the x-axis with all distances, lengths, and angles preserved. If a point is 6 units above the x-axis, it will reflect and now be 6 unis below the x-axis and so forth.
Oh ok. Sweet! Thanks!! That makes perfect sense!
Glad it does :)