TEXT BOOK, PAGE 574 # 5:
QUESTION: Use the transformation T: (x, y) ---> (x + 1, y +2) in this exercise.
a. Plot the following points and their images on the chalkboard: A (0, 0), B (3, 4), C (5, -1), and D (-1, -3).
[Hint: Obviously, we should use graph paper to plot the points.Label the original points and label each image on the graph paper.
Example A is (0, 0); so A' is (0 + 1, 0 + 2). That is, we have A' (1, 2) as the image of A. Do each point like that.]
b. Find AB, A'B', CD, and C'D'.
[Hint: Use the distance formula. It's in our textbook.]
c. Does this transformation appear to be an isometry?
[Hint: What is an isometry? Look in the class notes. ]
d. What is the preimage of (0, 0) and (4, 5)?
[Hint: Use the rule and solve the equation involved. For example, if we want to find the preimage of (7, 10), we would let x + 1 = 7, and y + 2 = 10. Then we would get that x = 6, and y = 8, and so the preimage of (7, 10) would be (6, 8).]
TEXT BOOK, PAGE 580 # 1, 5, 6.
[HINT: We just draw the given images as a reflection through the given lines. #6 is different from the rest. How?]
TEXT BOOK, PAGE 586 # 3, 6, 11
3. [HINT: First find the translation rule. by solving 0 + a = 5, and 0 + b = 1. Then add a to 3 and b to 3 to get the answer (3 + a, 3 + b) = (, ). This is how we do all these types of problems. In this case, the calculation was unnecessary, but it is not always like that.]
6. [Hint: Use the method of # 3 to find a and b. After we find a and b, do we add or subtract? Think.]
11. [Hint: Invariant means "does not change"? (a) Does the distance between points ("length of segments") on the image change when an image is translated? That is, if a triangle has side AB = 4cm, would A'B' have the same length? (b) If angle ABC is 60 degrees, would angle A'B'C' have the same measure? (c) Would triangle A'B'C' have the same area as triangle ABC? (d) Orientation: This means that if we move in a counter-clockwise direction when moving from vertex A to vertex B to vertex C on the triangle, would we still move in a counter-clockwise position when moving from vertex A' to B' to C' in the image? Does translation flip the triangle or does it keep it
the same? No flip means no change in orientation. Flip means change in orientation.]
TEXT BOOK PAGES 590 - 591 # 4, 7, 9
4. [HINT: Add any multiple of 360 to -720 to get an equivalent rotation.
7. [Remember: -60 means a rotation 60 degrees in what directions? That is, is this 60 degrees counterclockwise, or is it 60 degrees clockwise?]
32. (a), (b), and (c) can be done with very little stress if we use our class notes, or look up material that we covered already in the textbook.
(d).[HINT: The theorem is a theorem about preservation of distance. Write a sentence using the words "isometry" and "rotations (or "rotations")).]
(e)[HINT: What do you know about triangles ABC and A'B'C' in terms of congruence? How do the areas of congruent figures compare?]
(f) [HINT: We already know the rule for R (x, y) 90 degrees in the origin. We have that rule in our class notes. Just copy the rule.]
I will return with HINTS FOR THE QUESTION FROM HANDOUT C before the week is up.
ENJOY THE REST OF YOUR SPRING BREAK!
Mr. Wellington
QUESTION: Use the transformation T: (x, y) ---> (x + 1, y +2) in this exercise.
a. Plot the following points and their images on the chalkboard: A (0, 0), B (3, 4), C (5, -1), and D (-1, -3).
[Hint: Obviously, we should use graph paper to plot the points.Label the original points and label each image on the graph paper.
Example A is (0, 0); so A' is (0 + 1, 0 + 2). That is, we have A' (1, 2) as the image of A. Do each point like that.]
b. Find AB, A'B', CD, and C'D'.
[Hint: Use the distance formula. It's in our textbook.]
c. Does this transformation appear to be an isometry?
[Hint: What is an isometry? Look in the class notes. ]
d. What is the preimage of (0, 0) and (4, 5)?
[Hint: Use the rule and solve the equation involved. For example, if we want to find the preimage of (7, 10), we would let x + 1 = 7, and y + 2 = 10. Then we would get that x = 6, and y = 8, and so the preimage of (7, 10) would be (6, 8).]
TEXT BOOK, PAGE 580 # 1, 5, 6.
[HINT: We just draw the given images as a reflection through the given lines. #6 is different from the rest. How?]
TEXT BOOK, PAGE 586 # 3, 6, 11
3. [HINT: First find the translation rule. by solving 0 + a = 5, and 0 + b = 1. Then add a to 3 and b to 3 to get the answer (3 + a, 3 + b) = (, ). This is how we do all these types of problems. In this case, the calculation was unnecessary, but it is not always like that.]
6. [Hint: Use the method of # 3 to find a and b. After we find a and b, do we add or subtract? Think.]
11. [Hint: Invariant means "does not change"? (a) Does the distance between points ("length of segments") on the image change when an image is translated? That is, if a triangle has side AB = 4cm, would A'B' have the same length? (b) If angle ABC is 60 degrees, would angle A'B'C' have the same measure? (c) Would triangle A'B'C' have the same area as triangle ABC? (d) Orientation: This means that if we move in a counter-clockwise direction when moving from vertex A to vertex B to vertex C on the triangle, would we still move in a counter-clockwise position when moving from vertex A' to B' to C' in the image? Does translation flip the triangle or does it keep it
the same? No flip means no change in orientation. Flip means change in orientation.]
TEXT BOOK PAGES 590 - 591 # 4, 7, 9
4. [HINT: Add any multiple of 360 to -720 to get an equivalent rotation.
7. [Remember: -60 means a rotation 60 degrees in what directions? That is, is this 60 degrees counterclockwise, or is it 60 degrees clockwise?]
32. (a), (b), and (c) can be done with very little stress if we use our class notes, or look up material that we covered already in the textbook.
(d).[HINT: The theorem is a theorem about preservation of distance. Write a sentence using the words "isometry" and "rotations (or "rotations")).]
(e)[HINT: What do you know about triangles ABC and A'B'C' in terms of congruence? How do the areas of congruent figures compare?]
(f) [HINT: We already know the rule for R (x, y) 90 degrees in the origin. We have that rule in our class notes. Just copy the rule.]
I will return with HINTS FOR THE QUESTION FROM HANDOUT C before the week is up.
ENJOY THE REST OF YOUR SPRING BREAK!
Mr. Wellington
