Page 15


Problem 1


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Problem 2


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Problem 3


The equation of the line with intercepts (a,0) and (0,b) is bx+ay=ab

The line y=x intersects this line at the point





Problem 4


This is a question of, "When is B on the line through A and B?"

This is about SLOPE! Solve the following equation (where did it come from?)



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Problem 5


This applet will suggest a path to finding a solution. You could also try substitution. What could you substitute in for x? What could you substitute in for y?

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Problem 6


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Problem 7


I have never been able to solve this problem in 5 years of doing it.



Problem 8


This is a question about intercepts. The x and y intercepts (respectivley) of the line 2x-3y=18 are (9,0) and (0,-6). The intercepts of the line 2x-3y=24 are (12,0) and (0,-8). Therefore, you could move the first line DOWN 2 units corresponding to a vector [0,-2], or you could move the first line RIGHT 3 units, corresponding to a vector [3,0]. Of course, there are many other answers. As long as you can map one point to another point without tilting the line, you have found a translation.

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Problem 9


Graph it. The resulting triangle is an isosceles right triangle, making the angles 45 degrees.



Problem 10 and 11


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Problem 12


Drag the red points around. Why do each of these rectangles satisfy the conditions of the problem?

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Page 16


Problem 1


(a) [2,-9] (b) [3,-4] (look at part b as (2,3) + t[3,-4] )



Problem 2


(a) [-1,4] (b) [1,-4] (these two vectors oppose each other)



Problem 3




is half as long as



and is the same vector as



even though they start at different points, and is just the opposite of





Problem 4


Do not be lazy. Choose numbers for m and that meet the conditions of the problem (positive integers with m<n ) and find the values of x, y, and z. Then study these numbers carefully. Do you see a pattern? If not, repeat with new values for m and n.

Then, try and prove a general result.



Problem 5


Graph these four lines in GeoGebra, and look at the resulting shape. A rhombus is an equilateral parallelogram. Does this quadrilateral meet the conditions?



Problem 6, 7 and 8

These are just congruent triangle things. Do them and we will talk about them.



Problem 9


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Problem 10


Why don't YOU try to set this up in GeoGebra and see how the points are related? Create a slider called t, and use the slider to control three different points, one for part (a), one for part (b), and one for part (c). Once you create this, embed in your wiki page so I can see it!



Problem 11


If they have just passed each other, there is a difference of 13 seconds in the time it takes to complete a lap. Which means, each lap Avery runs, he makes up 1/6 of a lap. So 6x78 seconds is the time it will take to pass him again.