The radius of a circle with this equation is _____?
x^2 - 10x + y^2 - 6y = -9
OK, we just did equations for circles in the previous chapter, Lesson 11-3. We know that this will appear on the SBAC, so this problem is worth doing. We'll complete the square:
x^2 - 10x + y^2 - 6y = -9
x^2 - 10x + 5^2 + y^2 - 6y + 9 = -9 + 9 + 5^2
(x - 5)^2 + (y - 3)^2 = 5^2
And so our circle has center (5, 3) and radius 5. Therefore our desired radius is 5 -- and of course, today's date is the fifth.
Lesson 12-3 of the U of Chicago text is called "Properties of Size Changes." In the modern Third Edition of the text, properties of size changes appear in Lesson 12-1.
This is what I wrote last year about today's lesson. Admittedly it isn't much.
Finally, here are the Geometry worksheets for today. They are based on Lesson 12-3, with an extra page for the proof of the Dilation Distance Theorem -- this proof comes directly from PARCC.
And I have nothing much else to say. So this is one of my shortest posts of the year!
EDIT: I changed this post one day late in order to eliminate the old reference to PARCC. I actually found an old version of the second page of this worksheet saved on my computer, and so I include it as the new second page.
Meanwhile, the old first page makes an reference to FTS (an old Hung-Hsi Wu proof). Even though I no longer include Wu's FTS as part of the lesson, it's actually too much work to redo the entire page just to get rid of two little FTS mentions (especially when I'm already posting this late). So you'll just have to ignore FTS.
(x - 5)^2 + (y - 3)^2 = 5^2
And so our circle has center (5, 3) and radius 5. Therefore our desired radius is 5 -- and of course, today's date is the fifth.
Lesson 12-3 of the U of Chicago text is called "Properties of Size Changes." In the modern Third Edition of the text, properties of size changes appear in Lesson 12-1.
This is what I wrote last year about today's lesson. Admittedly it isn't much.
Finally, here are the Geometry worksheets for today. They are based on Lesson 12-3, with an extra page for the proof of the Dilation Distance Theorem -- this proof comes directly from PARCC.
And I have nothing much else to say. So this is one of my shortest posts of the year!
EDIT: I changed this post one day late in order to eliminate the old reference to PARCC. I actually found an old version of the second page of this worksheet saved on my computer, and so I include it as the new second page.
Meanwhile, the old first page makes an reference to FTS (an old Hung-Hsi Wu proof). Even though I no longer include Wu's FTS as part of the lesson, it's actually too much work to redo the entire page just to get rid of two little FTS mentions (especially when I'm already posting this late). So you'll just have to ignore FTS.
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