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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 4 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. plot the points on new coordinates after the flood

You have gone viral after your video received 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.

5 pointers are placed at A : -2,0. B : 0,0. C : 0,2. D : -1,3. E : -2,2.

Multiply 2 by each x and u, example (2x, 2y)

answer choices: 4,4. 6,10. 4,8. 8,8. 8,4.

.4 Plot the new coordinates from the above action. Make sure you note the dilatation 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.

2 answers

Let's walk through the exercise step-by-step.

Step 1: Original Coordinates

You are asked to plot the original points of your house in the new housing development:

  • A(2, 2)
  • B(4, 2)
  • C(4, 4)
  • D(3, 5)
  • E(2, 4)

Make sure to place these points accurately on the graph provided.

Step 2: Moving Your House

Next, you need to calculate the new coordinates after the flood, which moves your house 4 blocks to the left and 2 blocks down.

To calculate the new coordinates:

  • For Point A(2, 2):

    • New x-coordinate = 2 - 4 = -2
    • New y-coordinate = 2 - 2 = 0
    • → A(-2, 0)

  • For Point B(4, 2):

    • New x-coordinate = 4 - 4 = 0
    • New y-coordinate = 2 - 2 = 0
    • → B(0, 0)

  • For Point C(4, 4):

    • New x-coordinate = 4 - 4 = 0
    • New y-coordinate = 4 - 2 = 2
    • → C(0, 2)

  • For Point D(3, 5):

    • New x-coordinate = 3 - 4 = -1
    • New y-coordinate = 5 - 2 = 3
    • → D(-1, 3)

  • For Point E(2, 4):

    • New x-coordinate = 2 - 4 = -2
    • New y-coordinate = 4 - 2 = 2
    • → E(-2, 2)

So the new coordinates after the flood are:

  • A(-2, 0)
  • B(0, 0)
  • C(0, 2)
  • D(-1, 3)
  • E(-2, 2)

Identifying the Correct Choice

Among the given choices for the new coordinates, the correct answer is:

  • A(-2, 0), B(0, 0), C(0, 2), D(-1, 3), E(-2, 2)

Step 3: Plot the New Coordinates

You would now plot these new coordinates on the graph.

Step 4: Doubling the Size of the House

Now, you want to double the size of your house using the new coordinates after the flood. Each coordinate will be multiplied by 2:

New coordinates:

  • A(-2, 0) → (-22, 02) = (-4, 0)
  • B(0, 0) → (02, 02) = (0, 0)
  • C(0, 2) → (02, 22) = (0, 4)
  • D(-1, 3) → (-12, 32) = (-2, 6)
  • E(-2, 2) → (-22, 22) = (-4, 4)

The new coordinates after doubling are:

  • A(-4, 0)
  • B(0, 0)
  • C(0, 4)
  • D(-2, 6)
  • E(-4, 4)

Choices for the New Coordinates

From the previous calculations, the possible answers (using the doubling coordinates) are:

  1. A(-4, 0)
  2. B(0, 0)
  3. C(0, 4)
  4. D(-2, 6)
  5. E(-4, 4)

This does not directly match the answer choices given (4,4), (6,10), (4,8), (8,8), (8,4) — it seems like a misunderstanding of the problem setup, or the answer choices listed do not directly correlate to these new coordinates. If you need a specific choice, focus on what aligns correctly with the transformations discussed.

Step 5: Plotting the Final Coordinates

Lastly, plot these new coordinates on the graph to show how the size of your house was enlarged through dilation.

Explanation of Dilation

Dilation in this context refers to scaling the coordinates of your house by a factor of 2 while maintaining the relative positions. It enlarges the shape of the house without changing its proportions or basic structure. Each point of the house moves away from the origin proportionally, creating a larger version of the original house shape.

Make sure to compare this new plot with the original coordinates to visualize the difference in size after the dilation.

1. A figure in the plane has this if the figure can be mapped onto itself by a rotation of 180 degrees or less. What is it?

2. A type of composite or combination transformation of a reflection over a line followed by a translation or vice versa. What is it?

3. the operation that maps, or moves, a preimage onto an image. What is it?

4. A line that a figure in the plane has if the figure can be mapped onto itself by a reflection in the line. What is it?

5. Also known as the angle of rotation; the measure of degrees that a figure is rotated about a fixed point. What is it?