Page 19


Problem 1


This problem is all about using the formula for the area of a triangle to find other information about the triangle.

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Problem 2


Let s be my cycling speed. Using the concept of d=rt, we have



and



Since the distance for these two situations are the same (why?), you should solve the following system:





Problem 3 and 4


Begin by completing these triangles. Show they are congruent by SSS, then appeal to CPCTC.
For #4, use SAS.

page19_problem3.png



Problem 5


When asking for a point equidistant from two points, I recall that I am looking for a point on the perpendicular bisector of the two points. This point must also be on the line x+2y=8.

Recall that to find the equation of the perpendicular bisector of (3,8) and (9,6), you need to find the slope of the segment connecting these two points (m=-1/3). The perpendicular bisector has a slope of 3. It passes through the midpoint of the segment (6,7). I then use the point-slope form of a line to write the equation: y-7=3(x-6) or y=3x-11.

Now you need to find where this line intersects the line x+2y=8.



Problem 6


You have done this problem or problems like this a gazillion times.



Problem 7


Look back for the square in a right triangle on a graph problem.



Problem 8


The question is asking for the time I can walk before I begin running, so let's define some variable to reflect this.

Let t=time spent walking. Then the time spent running is 1/6 - t (why?)

Therefore



Which leads to a solution of





You should try to construct drag-testable figures shown in the next two applets!

Problem 9


Play around with this applet of an equilateral quadrilateral and its diagonals. Do the diagonals look perpendicular? How can you explain why or why not by only using the fact that the sides are congruent?

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Problem 10


Play around with this applet.

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Page 20


Problem 1


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Problem 2


Well? What are you waiting for? Post your problems and solutions on THIS PAGE! Yes...this is for a grade. Be certain to include your name with the problem.



Problem 3


Drag points A, B, and C to the points in the problem. Check your equations for the perpendicular bisectors shown in the applet. Once you have done this, drag K around until the distances are the same. What do you notice? Repeat this for some different locations of A, B, and C. Make a conjecture: "The point equidistant from three points is found by..."

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Problem 4




Problem 5


You should do the problem on paper first. Then play around with this applet. I have given you enough tools to create the reflection line (if you remember how we found it two weeks ago). The BIG questions is: When given a mirror line, how can I write the transformation as a coordinate rule?

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Problem 6


Play around with this applet. The quadrilateral shown meets the conditions of the problem (the Givens). Look for congruent triangles in the figure.

What kind of figure is it? Can you prove it?

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Problem 7


If Whitney traveled from (-2,3) to (10,8) in one hour, she is travels



In 35 minutes, she travels a distance of



After 35 minutes, she is located at the point






Problems 8, 9, and 10

8


Find any two points on the line 2x+5y=8, and draw a vector from one point to the other. This is a direction vector. For example, the points (4,0) and (-1,2) are on the line (How do you know THAT??). A vector from one to the other is [-5,2] or [5,-2]. All of our vectors should "reduce" to one of these two vectors.

9


If the vector [b,-a] is a direction vector for the line ax+by=c, and if (m,n) is a point on the line, then (m+b,n-a) is another point on the line. Substitute this other point into the line equation

a(m+b)+b(n-a)=am+ab+bn-ba=am+bn=c (because (m,n) is on the line.

This means that [b,-a] is a direction vector.

10






Problem 11


You have done this problem a gazillion times, too.

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