A house is
A (2,2)
B (4,2)
C (4,4)
D (3,5)
E (2, 4)
A flood moves your house exactly 4 blocks to the left and 2 blocks down. Is your new house after this transformation congruent to the original house?
No, the new house after this transformation is not congruent to the original house.
explain your answer
To determine if two figures are congruent, we need to compare their corresponding sides and angles. In this case, the original house has side lengths of AB = 2, BC = 2, CD = sqrt(2), DE = sqrt(2), and EA = sqrt(2).
However, after the flood moves the house 4 blocks to the left and 2 blocks down, the new house has side lengths of A'B' = 2, B'C' = 2, C'D' = sqrt(2), D'E' = sqrt(2), and E'A' = sqrt(2).
Comparing the corresponding sides, we can see that AB ≠ A'B', BC ≠ B'C', CD ≠ C'D', DE ≠ D'E', and EA ≠ E'A'. Therefore, the new house is not congruent to the original house.
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) .
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.
Is your new house after this transformation congruent to the house after the flood.
To plot the points of the new house after a scale factor of 2, we will multiply the x and y coordinates of each point by 2. The new coordinates for the house are:
(-8, 0), (-8, 8), (-4, 12), (0, 8), and (0, 0).
We will plot these points on a graph, using a different color than the original house. Let's use the color blue for the new house.
Now, to determine if the new house after the dilation is congruent to the house after the flood, we need to compare their corresponding sides and angles.
Starting with the original house after the flood:
AB = 2 units, BC = 2 units, CD = sqrt(2) units, DE = sqrt(2) units, and EA = sqrt(2) units.
Comparing these side lengths to the new house after the dilation:
A'B' = 8 units, B'C' = 8 units, C'D' = 4*sqrt(2) units, D'E' = 4*sqrt(2) units, and E'A' = 4*sqrt(2) units.
As we can see, the corresponding sides of the two houses are not equal. Therefore, the new house after the dilation is not congruent to the house after the flood.
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, coordinates are; (-4,0), (-4,4), (-2,6), (0,4), and (0,0).
With a different color, plot and state the points of your neighbor's house, which is a reflection of your house coordinates; (-4,0), (-4,4), (-2,6), (0,4), and (0,0) over the y-axis.
Is your new house after this congruent to the house of coordinates; (-4,0), (-4,4), (-2,6), (0,4), and (0,0)? Explain your answer
To plot the points of the neighbor's house, which is a reflection of your house over the y-axis, we need to change the sign of the x-coordinates while keeping the y-coordinates the same. The new coordinates for the neighbor's house are:
(4, 0), (4, 4), (2, 6), (0, 4), and (0, 0).
We will plot these points on a graph, using a different color than the original and dilated houses. Let's use the color green for the neighbor's house.
Now, to determine if your new house after the dilation is congruent to the neighbor's house, we need to compare their corresponding sides and angles.
Starting with your new house after the dilation:
A'B' = 8 units, B'C' = 8 units, C'D' = 4*sqrt(2) units, D'E' = 4*sqrt(2) units, and E'A' = 4*sqrt(2) units.
Comparing these side lengths to the neighbor's house:
A''B'' = 8 units, B''C'' = 8 units, C''D'' = 4sqrt(2) units, D''E'' = 4sqrt(2) units, and E''A'' = 4sqrt(2) units.
As we can see, the corresponding sides of the two houses are equal. Therefore, your new house after the dilation is congruent to the neighbor's house.
A tornado hit the area. It picked your house and rotated it 180 degrees counterclockwise.
Plot and state the points of your new house from Chapter 3 after a counterclockwise rotation of 180 degrees about the origin.
Is the new location of your house this transformation congruent to the neighbors house?
To plot the points of your new house after a counterclockwise rotation of 180 degrees about the origin, we need to switch the signs of both the x and y coordinates of each point in your original house.
The coordinates for the new house after the counterclockwise rotation are:
A'(-2, -2), B'(-2, -4), C'(-4, -4), D'(-5, -3), and E'(-4, -2).
We will plot these points on a graph, using a different color than the previous houses. Let's use the color purple for the new house.
Now, to determine if the new location of your house after this transformation is congruent to the neighbor's house, we need to compare their corresponding sides and angles.
Comparing the side lengths of your new house and the neighbor's house:
A'B' = 2 units, B'C' = 2 units, C'D' = sqrt(2) units, D'E' = sqrt(2) units, and E'A' = sqrt(2) units.
Comparing these side lengths to the neighbor's house:
A''B'' = 8 units, B''C'' = 8 units, C''D'' = 4*sqrt(2) units, D''E'' = 4*sqrt(2) units, and E''A'' = 4*sqrt(2) units.
As we can see, the side lengths of the two houses are not equal. Therefore, the new location of your house after this transformation is not congruent to the neighbor's house.