For fun, x=-1.what are the coordinates for F after a reflection? F(-5,5), U(-1,4), N(-3,0) Line of reflection is -1
To find the coordinates of point F after a reflection over the line x=-1, you need to consider the line as the mirror and find the same distance from the mirror line on the other side.
The reflection of a point over a vertical line, such as x=-1, results in a new point with the same y-coordinate as the original point. However, the x-coordinate changes sign.
So, if the original coordinates of F are (-5, 5), the reflection of F over x=-1 would have the coordinates (5, 5).
Note that the coordinates of points U and N are not required for finding the reflection of F.
To reflect a point across a line, we can use the formula:
x' = 2 * x_line - x
y' = 2 * y_line - y
Given that the line of reflection is x = -1, let's calculate the coordinates for point F(-5,5) after reflection.
For point F:
x' = 2 * (-1) - (-5)
y' = 2 * 0 - 5
Simplifying:
x' = -2 + 5 = 3
y' = -5
Therefore, after reflection, point F(-5,5) will have coordinates F'(3,-5).
Let me know if you have any other questions!
To find the coordinates of point F after a reflection, we first need to understand what a reflection is. A reflection is a transformation that "flips" a figure over a line. In this case, the line of reflection is x = -1.
To find the coordinates of a point after reflection over a line, we can follow these steps:
1. Draw a perpendicular line from the point to the line of reflection. This is called the "normal line."
2. Measure the distance between the point and the line of reflection.
3. Move the same distance on the other side of the line of reflection, along the normal line.
4. Find the intersection between the normal line and the line of reflection. This will be the reflected point.
Let's follow these steps to find the coordinates of point F after reflection:
1. Draw a perpendicular line from point F to the line of reflection (-1).
- The normal line is a line perpendicular to the reflection line and passes through the figure.
- In this case, since the line of reflection is vertical with the equation x = -1, the normal line would be horizontal. It will have a constant y-value of 5.
- So, draw a horizontal line passing through the point F(-5, 5).
2. Measure the distance between point F and the line of reflection.
- The distance can be computed by subtracting the x-value of the point from the x-value of the reflection line.
- In this case, the distance is: -1 - (-5) = 4.
3. Move the same distance on the other side of the line of reflection, along the normal line.
- Since the normal line has a constant y-value of 5, we need to add the distance (4) to the x-value of the reflection line (in this case, -1).
- So, the new x-value would be: -1 + 4 = 3.
4. Find the intersection between the normal line and the line of reflection.
- In this case, the intersection point with the normal line y = 5 and the reflection line x = -1 will give us the reflected point F.
- So, the reflected point F after the reflection is (3, 5).
Therefore, after reflecting point F(-5, 5) over the line x = -1, we get F'(3, 5).