You are just beginning your life as an adult and have bought a house in a new housing development. Your house is located at A (2,2), B (4,2), C (4,4), D (3,5), and E (2,4). A flood moves your house exactly 4 blocks to the left and 2 blocks down.
what are the new coordinates of your house?
The new coordinates of your house after the flood can be obtained by subtracting 4 from the x-coordinate and 2 from the y-coordinate of each original coordinate.
A: (2 - 4, 2 - 2) = (-2, 0)
B: (4 - 4, 2 - 2) = (0, 0)
C: (4 - 4, 4 - 2) = (0, 2)
D: (3 - 4, 5 - 2) = (-1, 3)
E: (2 - 4, 4 - 2) = (-2, 2)
So, the new coordinates of your house are A (-2,0), B (0,0), C (0,2), D (-1,3), and E (-2,2).
Describe specifically the formal transformation that occurred when the flood moved your house.
The flood moved your house through a translation transformation, shifting it 4 blocks to the left and 2 blocks down. Translation is a type of transformation that moves each point of an object in a specific direction by a certain distance.
In this case, the translation can be described as follows:
- All points of the original house were moved 4 blocks to the left, which means subtracting 4 from their x-coordinates.
- Additionally, all points were moved 2 blocks downwards, which means subtracting 2 from their y-coordinates.
This translation transformed the original house with coordinates A (2,2), B (4,2), C (4,4), D (3,5), and E (2,4) to the new house with coordinates A (-2,0), B (0,0), C (0,2), D (-1,3), and E (-2,2).
Is your new house after this transformation congruent to the original house? Explain your answer.
Yes, the new house after the translation transformation is congruent to the original house.
Congruence refers to having the same size and shape, and in this case, the translation transformation did not change the size or shape of the house. The original house and the new house have the same relative distances between their points, and all angles and side lengths remain unchanged.
While the specific coordinates of the points have changed, the overall geometric structure of the house remains the same. Therefore, the new house is congruent to the original house.
could you give a longer answer?
Of course! Let's explore the congruence between the original house and the new house after the translation transformation in more detail.
Congruence is determined by comparing the size and shape of two figures. In this case, we need to analyze if the original house and the new house have the same size and shape.
Size:
The size of a figure refers to its dimensions, such as side lengths or distances between points. In the translation transformation, the distance between each point of the original house and the corresponding point of the new house remains the same. For example, in both houses, the distance between points A and B, B and C, C and D, D and E, and E and A remains constant. Therefore, the size of the new house is identical to the original house.
Shape:
The shape of a figure relates to the arrangement of its points and the angles between its lines or edges. In the translation transformation, the relative positions and orientations of the lines and angles within the original house are maintained in the new house. This implies that the shape of the new house is the same as the original house.
In summary, the size and shape of the new house after the translation transformation are congruent to the original house. The translation transformation solely shifted the entire house in a specific direction without altering its dimensions or geometric structure. Therefore, both houses are identical in size and shape, fulfilling the criteria for congruence.
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.)
To plot the new points of the house after a scale factor of 2 with the given coordinates, we will multiply each x-coordinate and y-coordinate by 2.
Original Coordinates:
Point A: (2,2)
Point B: (4,2)
Point C: (4,4)
Point D: (3,5)
Point E: (2,4)
Coordinates after scaling by a factor of 2:
Point A: (2*2, 2*2) = (4, 4)
Point B: (4*2, 2*2) = (8, 4)
Point C: (4*2, 4*2) = (8, 8)
Point D: (3*2, 5*2) = (6, 10)
Point E: (2*2, 4*2) = (4, 8)
So, the new coordinates of the house after a scale factor of 2 are:
A: (4, 4)
B: (8, 4)
C: (8, 8)
D: (6, 10)
E: (4, 8)
Now let's plot these points on a coordinate plane:
-4 -2 0 2 4 6 8 10
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The new points of the house after the scale factor of 2 are plotted on the coordinate plane.