Certainly! Let's go through each question step by step:
Question 1:
You need to plot the points where your house is originally located, which are:
- A(2, 2)
- B(4, 2)
- C(4, 4)
- D(3, 5)
- E(2, 4)
Drop Points:
- A(2, 2)
- B(4, 2)
- C(4, 4)
- D(3, 5)
- E(2, 4)
Question 2:
After the flood, your house moves 4 blocks to the left and 2 blocks down. We calculate the new coordinates for each original point:
- A(2, 2): \( (2-4, 2-2) = (-2, 0) \)
- B(4, 2): \( (4-4, 2-2) = (0, 0) \)
- C(4, 4): \( (4-4, 4-2) = (0, 2) \)
- D(3, 5): \( (3-4, 5-2) = (-1, 3) \)
- E(2, 4): \( (2-4, 4-2) = (-2, 2) \)
So the new coordinates are:
- A(-2, 0)
- B(0, 0)
- C(0, 2)
- D(-1, 3)
- E(-2, 2)
Correct Response: New coordinates are A( -2, 0), B(0, 0), C(0, 2), D(-1, 3), E(-2, 2)
Question 3:
The transformation that occurred when the flood moved the house can be described as a translation. The entire set of coordinates moved left by 4 units and down by 2 units. This change resulted in a shift of each point in a consistent manner along the x and y axes, maintaining their relative positions to one another.
Question 4:
After the flood, plot the points based on the new coordinates:
- A(-2, 0)
- B(0, 0)
- C(0, 2)
- D(-1, 3)
- E(-2, 2)
You would select from the dropdowns shown in the tool or platform you are using to match the new coordinates accordingly.
Question 5:
To create a new house twice the size, we multiply each coordinate by 2:
- A(2, 2) → (22, 22) = (4, 4)
- B(4, 2) → (42, 22) = (8, 4)
- C(4, 4) → (42, 42) = (8, 8)
- D(3, 5) → (32, 52) = (6, 10)
- E(2, 4) → (22, 42) = (4, 8)
New Coordinates:
- 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)
Question 6:
The dilation transformed the original coordinates to the new coordinates by scaling each one by a factor of 2. This means that while the positions of the points relative to each other stayed the same, their distances from the origin increased, effectively enlarging the house.
Question 7:
The dilation took place when the coordinates were multiplied by 2, expanding the house size while keeping the shapes congruent. For example, transforming A(2,2) to A(4,4) means it was moved further away from the origin, maintaining the same form, just in a larger scale. All points were stretched equally, preserving their arrangement and distances relative to each other.
Question 8:
If a neighbor builds the same house across the street, the coordinates will be reflected across the y-axis. This changes the sign of the x-coordinates:
- A(4, 4) → A'(-4, 4)
- B(8, 4) → B'(-8, 4)
- C(8, 8) → C'(-8, 8)
- D(6, 10) → D'(-6, 10)
- E(4, 8) → E'(-4, 8)
Question 9:
The new transformation over the y-axis reflects the original coordinates across the line y-axis, changing each x-coordinate to its negative. The reflection maintains the congruence of the houses, meaning that despite the change in position, the shapes and sizes remain identical. Therefore, my neighbor's house is congruent to mine.
Question 10:
The definitions can be filled in as follows (assume you have a list to select from):
- Line of Symmetry: A line that divides a figure into two mirror-image halves.
- Reflection: A transformation creating a mirror image over a line.
- Rotation: A transformation that turns a figure around a fixed point.
- Rotation Symmetry: When a figure can be rotated and still look the same.
- Transformation: An operation that moves or changes a figure in some way.
- Translation: Moving a figure without changing its size, shape, or orientation.
- Isometry: A transformation that preserves distances and angles.
- Dilation: A transformation that changes the size of a figure.
- Pre Image: The original figure before transformation.
- Image: The figure after a transformation.
- Shrink: A dilation with a scale factor less than 1.
- Line of Reflection: The line over which a figure is reflected.
- Degree of Rotation: The measure of how far a figure is rotated.
- Clockwise: The direction of rotation that is the same as the hands of a clock.
- Scale Factor: The ratio of the size of the new figure to the original.
- Enlargement/Expansion: A dilation with a scale factor greater than 1.
Make sure to select and match each definition correctly in the platform you are using.