If you notice a mistake in a solution or a mispelling (get it?) you should do the following:
  1. Let me know
  2. Fix it yourself! After all, you can all edit these pages!

Page 17




Problem 1


page 17 problem 1
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Problem 2


Writing Robin's position as parametric equations, we have



From these equations, we see that Robin is moving 8 km right and 6 km up every hour. If Casey is 20 km behind, that means that Casey is 16 km LEFT and 12 km DOWN from Robin and any time. We can write this in two ways (though the first way is preferable):



or





Problem 3


(a) Look at the line y=1.3 or x=10.75 or y=x+7.1

(b) Only if the slope is irrational. For example,



(c) If it passes through two lattice points, the line has a rational slope and will pass through other lattice points.



Problem 4


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Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)



Problem 5 and 6


The vector from A to B is [-5,2]. Finding a vector that starts at C(4,3) and is perpendicular to [-5,2] means I need to step RIGHT 2 units and UP 5 units from C. Therefore, a point P that makes the vector from C to P perpendicular to the vector from A to B is P(6,8). The vector from C to P is [2,5].

Of course, and point on the line through A and P will do.



Problem 7


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)



Problem 8


Begin by trying to complete triangle ADF. Then, place a point at the midpoint of AC. Can you find another triangle that is congruent to ADF?
page17prob8.png



Problem 9


You have seen this problem before. This is a question of SLOPES! Solve the following proportion for x





Problem 10


C'mon! You try this one. I bet there is something strange waiting to happen.



Problem 11


Try to draw a picture of the cube unfolded.



Problem 12


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

You need to solve the system shown on the graph above for the coordinates of B. Then you need to find the time t that the bug is at B.



Solving this system, we find x=4.9. Looking at the parametric equations, we see that x(t) = 6-t, so 4.9 = 6 - t, or t=1.1 seconds.



Problem 13


page 17 problem 13
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Problem 14


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

From looking at the applet, it looks as if the paths are parallel. Looking at the parametric equations, both paths have a slope of 2. Also, it looks as if point Q moves much faster than P. Looking at the parametric equations, point Q moves with a speed of



units of distance per unit of time and P moves



units of distance per unit of time, which means Q is moving 3 times as fast.



Page 18


Problem 1


In the fourth line, writing



would have been incorrect because this statement implies that angle ABC is congruent to angle ACD (corresponding parts of congruent triangles are congruent), when angle ABC is actually congruent to angle ADC.



Problem 2


Angle ABC and Angle ADC are congruent by CPCTC (corresponding parts of congruent triangles are congruent). Simply replace the line five in the proof by this statement.



Problem 3