Transformations and Congruence Portfolio
Math 8 Q3 (Pre-Algebra) / Transformations and Congruence
Question 7
With a different color, plot and state the points of your neighbor’s house, which is a
reflection of your house in Chapter 3 over the y-axis. Name the color you use on your graph here.
please explain your answer and write it in first person
To plot the points of my neighbor's house, which is a reflection of my house over the y-axis, I will use a different color on my graph, let's say green.
First, I will identify and plot the points of my house on the graph. Let's assume the coordinates of my house are:
Point A: (2, 4)
Point B: (3, 5)
Point C: (1, 3)
Point D: (4, 6)
I will mark these points on the graph using my chosen color (let's say blue). Now, to reflect these points over the y-axis, I need to find their corresponding points on the opposite side.
To perform a reflection over the y-axis, I need to change the sign of the x-coordinate while keeping the y-coordinate the same. For example, the reflection of point A will be (-2, 4).
Using the same method, the reflections of the remaining points are as follows:
Reflection of point B: (-3, 5)
Reflection of point C: (-1, 3)
Reflection of point D: (-4, 6)
I will plot these reflected points on the graph using the chosen color, green. Now, I can connect the points to form the shape of my neighbor's house.
By using a different color, I can clearly distinguish between my house and my neighbor's house on the graph. This allows for a better visualization of the reflection over the y-axis.
Question 8
Is your new house after this transformation congruent to the house in Chapter 3?
Explain your answer.
No, my new house after this reflection over the y-axis is not congruent to the house in Chapter 3.
Congruence means that two figures have the same shape and size. In this case, my neighbor's house is a reflection of my house, which means it is flipped horizontally. As a result, the shape of my neighbor's house is the mirror image of my house.
Since congruent figures have the same shape and size, the reflection over the y-axis changes the orientation of the house, making it different from the original house in Chapter 3. Therefore, the new house after this transformation is not congruent to the house in Chapter 3.
A tornado hit the area. It picked up your house and rotated it 180 degrees
counterclockwise.
Question 9
Plot and state the points of your new house from Chapter 3 after a counterclockwise
rotation of 180 degrees about the origin. Use a different color to plot the points.
Name the color you use on your graph here.
To plot the points of my new house after a counterclockwise rotation of 180 degrees about the origin, I will use a different color on my graph, let's say purple.
First, I will identify and plot the points of my house from Chapter 3 on the graph. Let's assume the coordinates of my house are:
Point A: (2, 4)
Point B: (3, 5)
Point C: (1, 3)
Point D: (4, 6)
I will mark these points on the graph using a chosen color (let's say blue). Now, to rotate these points counterclockwise by 180 degrees about the origin, I need to find their new coordinates.
To perform a rotation of 180 degrees counterclockwise about the origin, I need to switch the sign of both the x and y coordinates. For example, the rotation of point A will be (-2, -4).
Using the same method, the rotations of the remaining points are as follows:
Rotation of point B: (-3, -5)
Rotation of point C: (-1, -3)
Rotation of point D: (-4, -6)
I will plot these rotated points on the graph using the chosen color, purple. Now, I can connect the points to form the shape of my new house after the counterclockwise rotation.
By using a different color, I can clearly distinguish between my original house and the rotated house on the graph. This allows for a better visualization of the rotation about the origin.
Question 10
Is the new location of your house after this transformation congruent to the
neighbor’s house in Chapter 4? Explain your answer
No, the new location of my house after the counterclockwise rotation of 180 degrees about the origin is not congruent to the neighbor's house in Chapter 4.
Congruence means that two figures have the same shape and size. In this case, the counterclockwise rotation changes both the orientation and the position of my house. It is important to note that the rotation is centered at the origin.
Even though the shapes of my house and the neighbor's house in Chapter 4 may be similar, the counterclockwise rotation has shifted my house to a new location. While the shape may remain the same, the sizes of the houses could differ.
Therefore, the new location of my house after this transformation is not congruent to the neighbor's house in Chapter 4.