Math 511 – Fall 2009 – Dr. Wright – Problems for Week 4
PROBLEM 4-1
Draw the reflection of figure ABC using the line l as the line of reflection. Label the corresponding points of your figure A’, B’, C’ and give their coordinates.
A’ ___(4,2)_____
B’ ___(2,8)______
C’ ___(-4,3)_____
What appears to be the “rule” describing the destination of a given point (x,y) after reflection in line l. Why is this reasonable? (Hint: What happens to the x- axis and the y axis after reflection in line l?
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PROBLEM 4-2
Draw the figure produced when triangle ABC is rotated 90 degrees clockwise about the origin. Label the corresponding points of this figure A3, B3, C3 and give their coordinates.
A3 ______
B3 ______
C3 ______
How is this problem related to the following fact: “perpendicular lines have negative reciprocal slopes”?
I am unfamiliar with the term “negative
Reciprocal slope”. If I try to break it down into terms I understand I think it would mean that the slope of the new line would be the opposite direction. So by looking at the drawing comparing line AC to Line A3C3 I can see started at (2,4) Line A3C3 started at (4,-2). Also Line AC ended at (3,-4) Line A3C3 3 ends at (-4, -3)
PROBLEM 4-3
Using the rectangular dot paper at the right, draw squares on the sides of triangle ABC. Each side of the given triangle will be one side of each of these squares.
What is the area of the square on side AB?
What is the area of the square on side BC?
What is the area of the square on side AC?
PROBLEM 4-4
a) Use the Pythagorean Theorem to find the altitude of triangle ABC below. Give an exact answer. Do not give an estimate or round off any numbers. Assume the horizontal distance between adjacent dots is 1 unit and the dots form equilateral triangles.
b) Find the area of triangle ABC