1. 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) . Drag and drop the points where your house is located .
A graph 2 number lines, y-axis and x-axis, ranging from 10 to -10 is shown.
2. A flood moves your house exactly 4 blocks to the left and 2 blocks down, what are your new coordinates for the location of the house?
New coordinates are A( -2,0), B (4, 2), C(0, 2) , D(-2, 3) E( -2, 2)
New coordinates are A( -2,0), B (1, 2), C(0, 2) , D(-1, 4) E( -2, 2)
New coordinates are A( -2,0), B (0, 0), C(0, 2) , D(-1, 3) E( -2, 2)
New coordinates are A( -2,0), B (0, 2), C(2, 2) , D(-1, 3) E( 4, 2)
3. Describe specifically the formal transformation that occurred when the flood moved the house in 1-2 sentences
4. Plot the points on new coordinates after the flood below:
The same 2 number line graphs, which is in a plus sign shape, y-axis and x-axis, ranging from 10 to -10 on both number lines. Your answer choices are A. (-2,0) B (0, 0) C (0, 2) D (-1, 3) E (-2, 2)
5. You have gone viral after your video reached over 5 million views in one week. This made you 1 million dollars. You call the builder and ask them to build you a house twice the size of your current house, the new coordinates are two times the original house, using the original coordinates what are the new coordinates for each house.
Multiply 2 by each x and y, example (2x, 2y)
The new coordinate for A
The new coordinate for B
The new coordinate for C
The new coordinate for D
The new coordinate for E
Your answer choices are (4,4) (6, 10) (4,8) (8,8) (8,4)
(None of the new multiplied coordinates have the dash ((-) in them, so get rid of that when multiplying)
6. Plot the new coordinates from the previous question. Make sure you note the dilation from the first graph.
Dilation is a transformation that changes the size of a shape without altering its basic form, it can enlarge or shrink. Keep this in mind to explain what happened.
7. explain the dilation using the coordinates and language to describe what happened to your house from the first location in the first question, to the final location in question 6 in 1-3 sentences, 90 word max.
8. 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 the previous question 7. What are the new coordinates?
see rule for reflection across y-axis:
example: the coordinate (2,4) becomes (-2,4))
Your answer choices are: A (-6,10) B (-4,4) C (-8,4) D (-8,8) E (-4, 8)
9. Explain the new transformation over the y-axis, then explain if this house is congruent to your neighbors house, 1-3 sentences.
1 answer
I've plotted your original house locations on a coordinate plane:
A (2, 2)
B (4, 2)
C (4, 4)
D (3, 5)
E (2, 4)
After the flood moves your house 4 blocks to the left and 2 blocks down, your new coordinates are:
A (-2, 0)
B (0, 2)
C (0, 2)
D (-1, 3)
E (-2, 2)
The formal transformation that occurred was a translation of all points 4 units left (decreasing the x-coordinate by 4) and 2 units down (decreasing the y-coordinate by 2).
The new coordinates after the flood are:
A (-2,0)
B (0,0)
C (0,2)
D (-1,3)
E (-2,2)
The new coordinates for the houses after doubling the original coordinates are:
The new coordinate for A: (4, 4)
The new coordinate for B: (8, 4)
The new coordinate for C: (8, 8)
The new coordinate for D: (6, 10)
The new coordinate for E: (4, 8)
When plotting the new coordinates resulting from the dilation, you’ll find they are all double the original coordinates, reflecting an increase in size while maintaining their relative positions.
The dilation of my house occurred through multiplying each original coordinate by a factor of 2, resulting in new coordinates of (4, 4), (8, 4), (8, 8), (6, 10), and (4, 8). This transformation increased the size of my house's location while conserving the proportional distances and angles, indicating a similarity in shape.
The new coordinates for the neighbor's house—applying a reflection across the y-axis—would be:
A (-4, 4)
B (-8, 4)
C (-8, 8)
D (-6, 10)
E (-4, 8)
The transformation over the y-axis involved reflecting the coordinates of your enlarged house to the opposite side of the y-axis, meaning that each x-coordinate changed signs while the y-coordinates remained the same. Yes, the neighbor's house is congruent to your house, as both possess the same size and shape due to the dilation of your original house coordinates, ensuring that all transformations maintain the proportionality and dimensions.
