A flood moves your house exactly 4 blocks to the left and 2 blocks down.
[The house would be here:
(-4, 2), (-4, 0), (-2, 0), (-2, 2), (-3, 3)]
Is your new house after this transformation congruent to the original house? (Which was (2,2), (4,2), (4,4), (3,5), and (2,4)]. Explain your answer.
No, the new house is not congruent to the original house.
Congruence means that two objects are identical in shape and size. The original house and the new house have the same shape, but they do not have the same size. The new house is smaller than the original house because it has been moved 4 blocks to the left and 2 blocks down.
Additionally, the coordinates of the new house are different from the coordinates of the original house. In the original house, the x-coordinate values increase from left to right, while in the new house, the x-coordinate values decrease from left to right.
Therefore, the new house is not congruent to the original house.
Describe specifically the formal transformation that occurred when the flood moved your house.
The formal transformation that occurred when the flood moved the house can be described as a translation.
Translation is a transformation that moves every point of an object the same distance in the same direction. In this case, the house was moved 4 blocks to the left and 2 blocks down.
The translation can be represented by the transformation rule: T(x, y) = (x - 4, y - 2).
Each point of the original house was shifted 4 units to the left on the x-axis and 2 units down on the y-axis to obtain the new coordinates of the house after the flood. The resulting coordinates (-4, 2), (-4, 0), (-2, 0), (-2, 2), and (-3, 3) represent the new location of the house after the translation.
You have become an internet sensation after your video received over 5 million views in one week. This made you 1 million dollars. You call a builder and ask them to build you a house twice the size of your current house. The new coordinates of your house are (–4,0), (–4,4), (–2, 6), (0,4), and (0,0). (These are the coordinates after a scale factor of 2)
Is your new house after this transformation congruent to the house in the first question? Explain your answer.
No, the new house is not congruent to the house in the first question.
Congruence means that two objects are identical in shape and size. While the new house has the same shape as the original house, it does not have the same size. The new house is twice the size of the original house as it was built to be twice the size.
The scale factor of 2 indicates that every side length and measurement of the original house has been multiplied by 2 to produce the dimensions of the new house. This means that the new house is larger in all aspects compared to the original house.
Therefore, the new house is not congruent to the house in the first question as it is much larger.
Because you are famous, people want to live near you. You have a new neighbor move in across the street after they build the same exact house as you did in Chapter 3.
Where would the plot points be (in ordered pairs) of your neighbor’s house? Reflecting your house in the previous question over the y-axis.
To reflect the plot points of your neighbor's house over the y-axis, we need to change the signs of the x-coordinates while keeping the y-coordinates unchanged.
The original coordinates of your neighbor's house were:
(-4, 0), (-4, 4), (-2, 6), (0, 4), and (0, 0).
Reflecting these points over the y-axis will change the signs of the x-coordinates, resulting in the new coordinates for your neighbor's house:
(4, 0), (4, 4), (2, 6), (0, 4), and (0, 0).
Therefore, the plot points (in ordered pairs) of your neighbor's house after reflecting your house over the y-axis would be:
(4, 0), (4, 4), (2, 6), (0, 4), and (0, 0).