Question 4
Is your new house after this transformation congruent to the original house? Explain
your answer.
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).
No, the new house is not congruent to the original house.
To determine congruency, we need to compare the corresponding sides and angles of both figures.
In the original house, the side lengths are:
AB = 4 units
BC = 6 units
CD = 4 units
DA = 2 units
In the new house, the side lengths are doubled:
AB' = 8 units
BC' = 12 units
CD' = 8 units
DA' = 4 units
Since the side lengths of the new house are double that of the original house, they do not match the original figure, and hence the new house is not congruent to the original one.
Question 5
Plot the points of the new house after a scale factor of 2 with the given coordinates.
(This is a transformation called dilation.) Use a different color to plot the points.
Name the color you use on your graph here.
I will plot the points of the new house after a scale factor of 2 using the color blue.
explain your answer
Apologies for the confusion. As an AI text-based model, I am unable to directly provide visual representations or create graphs. However, I can still describe how the points of the new house would be plotted after a scale factor of 2, using the given coordinates.
To plot the new house after the dilation, we would multiply each coordinate by 2. The new coordinates of the house would be:
(-4 * 2, 0 * 2) = (-8, 0)
(-4 * 2, 4 * 2) = (-8, 8)
(-2 * 2, 6 * 2) = (-4, 12)
(0 * 2, 4 * 2) = (0, 8)
(0 * 2, 0 * 2) = (0, 0)
Please note that the color blue was mentioned in the previous response for the purpose of distinguishing the plot of the new points from the original points on a graph. However, as an AI text-based model, I am not able to directly create or display visual representations.
Question 6
Is your new house after this transformation congruent to the house in Chapter 2?
Explain your answer.
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.
Based on the information provided, it is stated that the new neighbor built the "same exact house" as the transformed house in Chapter 3. This implies that the new neighbor's house has the same coordinates or dimensions as the transformed house.
If the new neighbor's house is indeed an exact copy of the transformed house, then it is congruent to the original house described in Chapter 2. This implies that the corresponding sides and angles of the two houses are equal, making them congruent.
please explain you answer
Apologies for the confusion. Let me clarify my response.
If the neighbor's house is an exact copy of the transformed house in Chapter 3, it means that both houses have the same dimensions, angles, and side lengths. In this case, the transformed house and the house described in Chapter 2 would be congruent.
To determine if the neighbor's house is congruent to the house in Chapter 2, we need to compare their attributes. If the coordinates, side lengths, and angles of the neighbor's house match those of the house in Chapter 2, then the two houses would be congruent.
However, without information about the exact coordinates, side lengths, or angles of both houses, it is not possible to definitively say whether the neighbor's house and the house in Chapter 2 are congruent. The congruency can only be determined by comparing specific attributes of both houses.