Do you location of the house is

Question

A(2,3) B(4,3) C(4,5) D(3,6) E(2,5)

A flood moves your house exactly 4 blocks to the left and 2 blocks down.
Plot and state the points of the new location of your house

Describe specifically the formal transformation that occured when the flood moved your house

Is your new house, after this translation, congruent to the original house? Explain your answer in a few words

Chapter 3
You have a new neighbor move in across the street from where your house is now located after the flood. They build the exact house as you have.

With a different color, plot and state the points of your neighbors house, which is a reflection of your house in Chapter 2 over the x-axis. Name the color you use on your graph here.

Is your neighbor's house congruent to your house? Explain your answer in a few words

Chapter4
A tornado hit the area. It picked up your house and rotated it 180 degrees counterclockwise

Question 7
Plot and state the points of your new house from Chapter 2 after a counterclockwise rotation of 180 degrees about the origin

Question 8
Is your house after this transformation congruent to the neighbor's house in Chapter 3? Explain your answer.

Answer 1

To answer your questions, let's break them down step by step:

Chapter 1

Original House Coordinates:

• A(2,3)
• B(4,3)
• C(4,5)
• D(3,6)
• E(2,5)

Transformation due to Flood:

• The flood moves your house 4 blocks to the left and 2 blocks down.
• This transformation can be expressed as subtracting 4 from the x-coordinates and 2 from the y-coordinates of each point.

New Location of Your House:

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

New Points of the House After Flood:

• A'(-2, 1)
• B'(0, 1)
• C'(0, 3)
• D'(-1, 4)
• E'(-2, 3)

Description of Transformation:

• The transformation that occurred when the flood moved your house can be described as a translation where each point was translated left by 4 units and down by 2 units.

Congruence:

• Yes, your new house (A', B', C', D', E') after this translation is congruent to the original house (A, B, C, D, E) because translation does not change the shape or size of the figure; it only changes the position.

Chapter 2

New Neighbor's House:

• Your neighbor's house is a reflection of your house over the x-axis.
• To reflect a point (x, y) over the x-axis, the new point becomes (x, -y).

Neighbor's House Coordinates (Reflection over the x-axis):

• A'(-2, 1) ⇒ A''(-2, -1)
• B'(0, 1) ⇒ B''(0, -1)
• C'(0, 3) ⇒ C''(0, -3)
• D'(-1, 4) ⇒ D''(-1, -4)
• E'(-2, 3) ⇒ E''(-2, -3)

New Points for Neighbor’s House:

• A''(-2, -1)
• B''(0, -1)
• C''(0, -3)
• D''(-1, -4)
• E''(-2, -3)

Color for Plot:

• For the neighbor’s house, let's say we use red on your graph.

Congruence with Neighbor's House:

• Yes, your neighbor's house is congruent to your house because reflection preserves the shape and size of the figure.

Chapter 3

Tornado Transformation:

• A tornado hits and rotates your house 180 degrees counterclockwise about the origin.
• The transformation of rotating a point (x, y) 180 degrees around the origin can be expressed as (-x, -y).

New Coordinates After Rotation:

• A''(-2, 1) ⇒ A'''(2, -1)
• B''(0, -1) ⇒ B'''(0, 1)
• C''(0, -3) ⇒ C'''(0, 3)
• D''(-1, -4) ⇒ D'''(1, 4)
• E''(-2, -3) ⇒ E'''(2, 3)

New Points After 180 Degrees Rotation:

• A'''(2, -1)
• B'''(0, 1)
• C'''(0, 3)
• D'''(1, 4)
• E'''(2, 3)

Question 8

Congruence with Neighbor's House:

• Yes, your house after the transformation (A''', B''', C''', D''', E''') is still congruent to your neighbor's house (A'', B'', C'', D'', E''). This is because rotation, like reflection, preserves shape and size.

In summary, your houses through the different transformations remain congruent because transformations like translations, reflections, and rotations maintain congruence in geometric figures.