Patrick Flaherty
Problem 1- Triangle ABC has points A(1,0) B(3,0) and C(3,5). If it were reflected across the y axis, and then translated along the vector <0,-5>, what would the coordinates of C'' be?
Problem 2- Pat builds models of WWII planes. If the original wingspan of a Grumman FF was 34' 6", and his model is 3' 10", what is the scale factor for this reduction?
Problem 2- Pat builds models of WWII planes. If the original wingspan of a Grumman FF was 34' 6", and his model is 3' 10", what is the scale factor for this reduction?
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Prashanth Gowda
Question: What is the perpendicular bisector of the following line?
Answer: y = (5/6)x + (7/12)
Work: m = (y2-y1)/(x2-x1)
m = (4 - -2)/(-2-3)
m = (6/-5)
y = mx + b
y = (-6/5)x + 2
Midpoint = ((x2+x1)/2,(y2+y1)/2)
Midpoint = ((-2 + 3)/2,(4 + -2)/2)
Midpoint = (1/2,2/2 )
Midpoint = (0.5,1)
Perpendicular Slope = (5/6)
y = (5/6)x + b
1 = (5/6)(1/2) + b
1 = (5/12) + b
b = 7/12
y = (5/6)x + (7/12)
Explanation: The first step is to find the equation of the original line. To find the equation, I need to know the slope(m) and the y-intercept(b). I found the slope by using the equation (y2-y1)/(x2-x1). After using this equation, I got that slope is (-6/5). I found the y-intercept by looking at the graph and seeing it intersects the y-axis at (0,2). Now I got the equation of the original line is y = (-6/5)x + 2. The next step is to find the midpoint of the original line. I need to find the midpoint of this line because that is where the perpendicular bisector intersects that line. I found the midpoint by plugging in the coordinates to the equation ((x2+x1)/2,(y2+y1)/2) and got the midpoint to be (0.5,1). Next I found the slope of the perpendicular bisector by finding the opposite reciprocal of the slope of the original line. I got the slope to be 5/6. Next I plugged the midpoint into the equation y=(5/6)x + b and got the y-intercept(b) to be 7/12. Finally I got the equation of the perpendicular bisector to be y = *5/6)x + (7/12).
Question: Problem 2- Juan wants to build a model Lamborghini Gallardo. In the model he made the overall length 5 times smaller than the actual car. If the model had an overall length of 34 inches, how long is the actual Lamborghini.
Answer: 170 inches
Work: Model - 1. 34 inches
2. model is 1/5 size of actual car
3. 34 x 5 =170 inches
Explanation: First I knew that the model's length was 34 inches. Then I knew that the model's length was 1/5 the size of the actual length. That means a scale factor of 1/5 was used to get from the actual car's length to the model's length. After I figured all of this out, I multiplied the model's length(35) by the scale factor of the model to the actual car(5) to get that the actual car's length was 170 inches.
Answer: y = (5/6)x + (7/12)
Work: m = (y2-y1)/(x2-x1)
m = (4 - -2)/(-2-3)
m = (6/-5)
y = mx + b
y = (-6/5)x + 2
Midpoint = ((x2+x1)/2,(y2+y1)/2)
Midpoint = ((-2 + 3)/2,(4 + -2)/2)
Midpoint = (1/2,2/2 )
Midpoint = (0.5,1)
Perpendicular Slope = (5/6)
y = (5/6)x + b
1 = (5/6)(1/2) + b
1 = (5/12) + b
b = 7/12
y = (5/6)x + (7/12)
Explanation: The first step is to find the equation of the original line. To find the equation, I need to know the slope(m) and the y-intercept(b). I found the slope by using the equation (y2-y1)/(x2-x1). After using this equation, I got that slope is (-6/5). I found the y-intercept by looking at the graph and seeing it intersects the y-axis at (0,2). Now I got the equation of the original line is y = (-6/5)x + 2. The next step is to find the midpoint of the original line. I need to find the midpoint of this line because that is where the perpendicular bisector intersects that line. I found the midpoint by plugging in the coordinates to the equation ((x2+x1)/2,(y2+y1)/2) and got the midpoint to be (0.5,1). Next I found the slope of the perpendicular bisector by finding the opposite reciprocal of the slope of the original line. I got the slope to be 5/6. Next I plugged the midpoint into the equation y=(5/6)x + b and got the y-intercept(b) to be 7/12. Finally I got the equation of the perpendicular bisector to be y = *5/6)x + (7/12).
Question: Problem 2- Juan wants to build a model Lamborghini Gallardo. In the model he made the overall length 5 times smaller than the actual car. If the model had an overall length of 34 inches, how long is the actual Lamborghini.
Answer: 170 inches
Work: Model - 1. 34 inches
2. model is 1/5 size of actual car
3. 34 x 5 =170 inches
Explanation: First I knew that the model's length was 34 inches. Then I knew that the model's length was 1/5 the size of the actual length. That means a scale factor of 1/5 was used to get from the actual car's length to the model's length. After I figured all of this out, I multiplied the model's length(35) by the scale factor of the model to the actual car(5) to get that the actual car's length was 170 inches.
Pavan Govu's Practice Problems
Problem #1
Question:Jordan, Dylan, and Aaroin are having an argument in math class. Based on the diagram below, they have to identify a pair of angles that are congruent. Jordan says that <A and <P are congruent. Dylan states <F and <G are congruent. Aaron believes that <P and <F are congruent. Who is wrong?
Answer and Explanation: To solve this problem, I first made a plan. I would take Jordan's statement and determine whether is is right or wrong using the knowledge I gained in Unit 2. Then, I would take Dylan's statement and determine whether it is right or wrong using the knowledge I gained in Unit 2. Then, I would take Dylan's statement and determine whether it is right or wrong using the knowledge I gained in Unit 2. Then, I would take Aaron's statement and determine whether it is right or wrong using the knowledge I gained in Unit 2. Then, to answer the question, I would find out who was wrong, and say that as my answer. After I had come up with a plan, I executed it, and took the first step. The question tells us that Jordan says <A and <P are congruent. After looking at the diagram, I observed that both angles were on the same side of the transversal and lie on the same side of the other lines. In Unit 2 Lesson 1, I learned that Corresponding Angles are angles that lie on the same side of the transversal and on the same side of the other two lines, so I can say that <A and <P are Corresponding Angles. In Unit 2 Lesson 1, I also learned that Corresponding Angles are congruent, so that means <A and <P are congruent, which makes Jordan correct. This tells us that Jordan is not the answer, because the question asks for the person who is wrong. Next, I moved on to Dylan and his statement. The question tells us that Dylan says <F and <G are congruent. After looking at the diagram, I observed that both angles were on the same side of the transversal but lie on opposite sides of the other lines. In Unit 2 Lesson 1, I learned that Same-Side Interior Angles are angles that lie on the same side of the transversal and on opposite sides of the other two lines, so I can say that <A and <P are Same-Side Interior Angles. In Unit 2 Lesson 1, I also learned that Same-Side Interior Angles are supplementary, so that means <A and <P are supplementary, which makes Dylan incorrect. This tells us that Dylan is the answer, if Aaron is correct, because the question asks for the person who is wrong. Lastly, to make sure that Dylan is the answer, I proceeded to check Aaron's statement. The question tells us that Aaron says <P and <F are congruent. After looking at the diagram, I observed that both angles were on opposite sides of the transversal and lie on opposite sides of the other lines. In Unit 2 Lesson 1, I learned that Alternate Interior Angles are angles that lie on the opposite sides of the transversal and are on opposite sides of the other two lines, so I can say that <F and <P are Alternate Interior Angles. In Unit 2 Lesson 1, I also learned that Alternate Interior Angles are congruent, so that means <F and <P are congruent, which makes Aaron correct. This tells us that Aaron is not the answer, because the question asks for the person who is wrong. From our findings, we can come to the conclusion that the answer to this question is Dylan.
Problem #2
Question: Candace lived on a coordinate plane. Her house was located at (1,1). Suddenly, her town's mayor wanted to build a mall exactly where her house was, so he told Candace that her house would have to be relocated. He also said, that the location of her new house would be determined by the vector, <2,3>. Which quadrant is Candace's new house located in?
Answer and Explanation: To solve this problem, I first created a plan. I would use the given vector to determine the location of Candace's new house. Then, based on it's coordinates, I would use the properties of each quadrant to find out which quadrant Candace's new house is located in. After coming up with a plan, I proceeded to execute it. First, I took the coordinates of Candace's house, which is given to us in the question as (1,1). Then, I interpreted what the vector meant. In the vector <2,3>, the x-value is positive, so that means we move 2 units to the right. The y-value is also positive, so that means we move 3 units up. This tells us that in order to find the coordinates of Candace's new house, we have to start from her original house and move 2 units to the right and 3 units up. This is the same as adding 2 to the x-value of the coordinates of Candace's original house, and adding 3 to the y-value of the coordinates of Candace's original house. So, since 2+1=3 & 3+1=4, the coordinates of Candace's new house is (3,4). Now that we now those coordinates, we can move on to the last step of answering our question. With the graph, we could simply plot the points and determine the quadrant Candace's new house is in, but there is another way of doint it too. Since the x-value in the coordinates of Candace's new house is positive, that means the house is on the right of the origin. Since the y-value in the coordinates of Candace's new house is positive, that means the house is above the origin. So Candace's new house is to above, and to the right of the origin, which leads us to our answer. Candace's new house, is in quadrant 1.