Graph the polygon and its image after a reflection in the line y=3.
*Here are the coordinates for polygon EFGH...
E(1,3)
F(4,3)
G(5,0)
H(2,0)
What are the coordinates for polygon EFGH after its reflection in the line y=3?
Please show all the work on how you got your answer.
If you plot the points you will totally see that the parallelogram has 2 vertices on the "flip" line and two below it.
The "flip" line is what you are reflecting over. So the ones on the line are "anchored" to the line and the two dots below the line flip over the line.
Let's look at (5,0)...
It is exactly 3 y coordinates below the line. So when you flip it over the line only the y coordinate will be affected. You will have to start at the line y=3 adn then add 3 to the y coordinate
(5, 3 is up at the line... ) but you want it reflected over the line
(5, 3 +3)
So (5,0) becomes (5,6) when reflected over the line y = 3
You do the other points : )
PS... you can see it nicely if you sketch it on the Cartesian Plane : )
Well, before we get into the reflection, let's take a moment to appreciate the geometry of this situation.
The line y=3 can be thought of as a balance beam for your polygon. Any point on the line would act as a fulcrum, causing the polygon to reflect or "flip" over the line.
Now, let's get to work and find the coordinates for the reflected polygon!
To reflect a point over a line, we need to visualize the process as a bouncing ball. You throw the ball at the line, it hits the line, and then bounces back on the opposite side. In our case, the polygon is the ball, and the line y=3 is the ground.
For each point (x, y), the reflection will have coordinates (x, 2c - y), where c is the y-coordinate of the line of reflection.
So for each point in the polygon EFGH, the y-coordinate will be flipped over the line y=3.
Let's do the calculations:
For point E(1, 3):
The y-coordinate of the line of reflection is 3.
Reflected coordinates will be (x, 2*3 - 3) = (x, 6 - 3) = (x, 3).
So, E becomes E'(1, 3).
For point F(4, 3):
The y-coordinate of the line of reflection is 3.
Reflected coordinates will be (x, 2*3 - 3) = (x, 6 - 3) = (x, 3).
So, F becomes F'(4, 3).
For point G(5, 0):
The y-coordinate of the line of reflection is 3.
Reflected coordinates will be (x, 2*3 - 0) = (x, 6 - 0) = (x, 6).
So, G becomes G'(5, 6).
For point H(2, 0):
The y-coordinate of the line of reflection is 3.
Reflected coordinates will be (x, 2*3 - 0) = (x, 6 - 0) = (x, 6).
So, H becomes H'(2, 6).
Therefore, the coordinates for the polygon EFGH after its reflection in the line y=3 are:
E'(1, 3)
F'(4, 3)
G'(5, 6)
H'(2, 6).
Now you have the reflected polygon coordinates. Safe and sound, thanks to the line y=3 acting as the polygon's personal trampoline!
To find the coordinates of the polygon EFGH after its reflection in the line y = 3, we need to understand the concept of reflection.
Reflection is a transformation that flips a shape across a line. In this case, we need to flip the polygon EFGH across the line y = 3.
To reflect a point (x, y) across the line y = 3, we can subtract the y-coordinate from 3 and keep the x-coordinate the same.
Let's find the coordinates of each point after reflection:
Point E(1, 3):
The y-coordinate of E is 3, which is equal to the line of reflection. So, the reflection of E will have the same x-coordinate, which is 1, and a y-coordinate equal to 3 - 3 = 0.
So, the reflection of E(1, 3) is E'(1, 0).
Point F(4, 3):
The y-coordinate of F is 3, which is equal to the line of reflection. So, the reflection of F will have the same x-coordinate, which is 4, and a y-coordinate equal to 3 - 3 = 0.
So, the reflection of F(4, 3) is F'(4, 0).
Point G(5, 0):
The y-coordinate of G is 0, which is below the line of reflection. To reflect it across the line y = 3, we need to calculate the distance from G to the line y = 3, which is 3 - 0 = 3.
Then, we negate this distance and add it to the y-coordinate of the line of reflection, which is 3. So, the y-coordinate of the reflection of G will be 3 - (-3) = 3 + 3 = 6.
The x-coordinate remains the same.
So, the reflection of G(5, 0) is G'(5, 6).
Point H(2, 0):
Similarly to G, the y-coordinate of H is 0, which is below the line of reflection. The distance from H to the line y = 3 is 3 - 0 = 3.
Negating this distance and adding it to the y-coordinate of the line of reflection, we get 3 - (-3) = 3 + 3 = 6.
The x-coordinate remains the same.
So, the reflection of H(2, 0) is H'(2, 6).
Therefore, the coordinates for the polygon EFGH after its reflection in the line y = 3 are:
E'(1, 0)
F'(4, 0)
G'(5, 6)
H'(2, 6).
To find the coordinates of the polygon after a reflection in the line y=3, we need to understand how reflection works.
1. The line of reflection is y=3. This means that every point on this line will remain fixed after reflection.
2. For points above the line, the reflection will be below the line. For points below the line, the reflection will be above the line.
Now, let's find the reflections of each point:
Point E(1,3): It lies on the line y=3, so its reflection will be the same point, (1,3).
Point F(4,3): It also lies on the line y=3, so its reflection will be the same point, (4,3).
Point G(5,0): It lies below the line y=3, so its reflection will be above the line. The distance between the point and the line y=3 is 3 units. So, we move the point 3 units above the line. The reflection of G will be (5,6).
Point H(2,0): It also lies below the line y=3. The distance between the point and the line y=3 is 3 units. So, we move the point 3 units above the line. The reflection of H will be (2,3).
Therefore, the coordinates for polygon EFGH after the reflection in the line y=3 are:
E' (1,3)
F' (4,3)
G' (5,6)
H' (2,3).
To graph the original polygon and its reflection, plot the points EFGH and E'F'G'H' on a coordinate plane and connect them to form the polygons.