Explain the dialation using the coordinates and language to describe what happened to your house from the first location in quesiton 1, to the final location in Question 6.

Question

QUESTION 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)

New coordinates are A( -2,0), B (0, 0), C(0, 2) , D(-1, 3) E( -2, 2)

QUESTION 6 Plot the new coordinates from the above action. Make sure you note the dialation 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.

final location
A (4,4) B (8,4) C (8,8) D (6,10) E (4,8)

Answer 1

To understand the dilation of your house from its original coordinates to its final coordinates, we'll analyze the coordinates step-by-step and explain what transformation occurred between the initial and final locations.

Initial Coordinates:

1. Point A: (2, 2)
2. Point B: (4, 2)
3. Point C: (4, 4)
4. Point D: (3, 5)
5. Point E: (2, 4)

New Coordinates After First Transformation:

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

Final Coordinates After Dilation:

1. Point A: (4, 4)
2. Point B: (8, 4)
3. Point C: (8, 8)
4. Point D: (6, 10)
5. Point E: (4, 8)

Dilation Analysis:

1. From Initial to New Coordinates (First Transformation):

   • The original set of points transforms to their new positions. This could potentially involve a change in location due to translation rather than dilation, where coordinates shifted across the axes. For instance, Point A moved from (2, 2) to (-2, 0). The specific transformation details are not provided, but we note that this could have involved a translation.

2. From New Coordinates to Final Coordinates (Dilation):

   • Now let's look at how we transform from the new coordinates to the final coordinates. Dilation requires a center point (in this context, we can consider origin (0,0) for simplicity) and a scale factor that determines how much to enlarge or shrink the shape.

   • Examining the transformations:

   • Scaling Factor:

     • When comparing the new location coordinates to the final coordinates:
       • For Point A: (-2, 0) becomes (4, 4). Here, it appears that we have scaled its x-coordinate by -2 (mirroring) and then multiplied by a factor approaching 2 to shift its position.
       • For Point B: (0, 0) becomes (8, 4). The x-coordinate increased, suggesting a significant dilation.
       • For Points C and D: a similar observation holds, as coordinates expand dramatically with the change in scale.

   • Estimates:

     • Each x-coordinate seems to be scaled approximately by 2. Points also appear to be moved, but the scaling demonstrates that the structure is retaining its shape while being enlarged.

Conclusion:

In summary, your initial house points underwent a translation that placed them in the new coordinates. Then, moving from the new coordinates to the final coordinates involved a dilation that enlarged the house significantly. The points represented a transformation that kept the same shape (i.e., the angles and ratios between points remain constant) but increased the size of the house in the coordinate plane. This maintains the original structure while allowing it to grow as represented by the final coordinates.

In visual terms, if you plotted all these points on a coordinate grid, the shape of your house would have maintained its overall structure despite the scaling and/or position changes that you identified at each step.