Question

Quadrilateral FGHI is reflected over a x = 1 of reflection to create F'G'H'I' . What are the coordinates of I'?

(-5,2)
(5,0)
(-3,2)
(-2,5)

Answer 1

tHE COORDINATES ARE F= (2,-2) g= (2,3) h= (3,3) i= (5,2)

Answer 2

To find the coordinates of point I' after reflecting point I over the line \( x = 1 \), we follow these steps:

1. Let's denote the coordinates of point I as \( (x, y) \).
2. The reflection of a point \( (x, y) \) over the line \( x = 1 \) can be found using the following formula:

\[
x' = 2 \times \text{line\_x} - x
\]
where \(\text{line\_x}\) is the x-coordinate of the line of reflection. In this case, \(\text{line\_x} = 1\).

3. The y-coordinate remains the same, so \( y' = y \).

Now, we need to evaluate the reflection for each of the given points to find point I's coordinates:

1. For point (-5, 2):

\[
x' = 2 \times 1 - (-5) = 2 + 5 = 7
\]
So, I' = (7, 2).

2. For point (5, 0):

\[
x' = 2 \times 1 - 5 = 2 - 5 = -3
\]
So, I' = (-3, 0).

3. For point (-3, 2):

\[
x' = 2 \times 1 - (-3) = 2 + 3 = 5
\]
So, I' = (5, 2).

4. For point (-2, 5):

\[
x' = 2 \times 1 - (-2) = 2 + 2 = 4
\]
So, I' = (4, 5).

Since none of the reflections provided give us a final point that matches those listed, it appears your point I wasn't specified. However, we calculate reflection for each and none reflected generate the points provided initially.

If you meant the original coordinates I are one of those listed, please specify which one so the exact reflection over x=1 can be reported back.

Answer 3

Given that point \( I = (5, 2) \), we will reflect it over the line \( x = 1 \).

1. **Identify the coordinates of point I:**

\[
I = (5, 2)
\]

2. **Use the reflection formula for the line \( x = 1 \):**

\[
x' = 2 \times 1 - x = 2 - 5 = -3
\]

The y-coordinate remains unchanged:

\[
y' = y = 2
\]

3. **Putting it together, the coordinates of the reflected point \( I' \) are:**

\[
I' = (-3, 2)
\]

Thus, the coordinates of point \( I' \) after reflection over the line \( x = 1 \) are:

\[
\boxed{(-3, 2)}
\]

This point \( (-3, 2) \) is not listed in your original options of coordinates \((-5, 2), (5, 0), (-3, 2), (-2, 5)\) but matches with \( (-3, 2) \).