Question

Triangle%C2%A0 PQR %C2%A0is reflected over a vertical line of reflection to create triangle%C2%A0 P′Q′R′ .%C2%A0What are the coordinates of point%C2%A0 R′ ?

Answer 1

When R preimage is (-11,1)

Answer 2

For%C2%A0 △FUN ,%C2%A0 x=−1 .%C2%A0What are the coordinates for F' after a reflection? (1 point) Responses F′(−1,4) upper F prime left parenthesis negative 1 comma 4 right parenthesis F′(3,5) upper F prime left parenthesis 3 comma 5 right parenthesis F′(5,−5) upper F prime left parenthesis 5 comma negative 5 right parenthesis F′(−5,−5)

Answer 3

To determine the coordinates of point R' after triangle PQR is reflected over a vertical line of reflection, we need to know the original coordinates of point R and the equation of the vertical line of reflection.

1. **Identify the vertical line of reflection**: Let's assume the line of reflection is given by the equation \( x = a \).

2. **Find the original coordinates of point R**: Let's say the coordinates of point R are \( (x_R, y_R) \).

3. **Determine the reflected coordinates**: When reflecting over a vertical line \( x = a \), the x-coordinate of the point R will change, while the y-coordinate will remain the same.

The new x-coordinate \( x_{R'} \) can be found using the formula:
\[
x_{R'} = 2a - x_R
\]
The y-coordinate remains the same:
\[
y_{R'} = y_R
\]

4. **Result**: Thus, the coordinates of point R' after reflection would be:
\[
R' = (2a - x_R, y_R)
\]

If you provide the original coordinates of R and the line of reflection, I can give you the exact coordinates of R'.

Answer 4

Given the coordinates of point \( R \) as \( (-11, 1) \), we need to reflect this point over a vertical line. Since you haven't provided a specific equation for the line of reflection, let’s assume \( x = a \) represents the vertical line of reflection.

1. **Original coordinates of \( R \)**:
\[
R = (-11, 1)
\]

2. **Reflection over the vertical line \( x = a \)**:

The formula to find the new x-coordinate after reflection over the line \( x = a \) is:
\[
x_{R'} = 2a - x_R
\]
where \( x_R = -11 \).

3. **New coordinates of \( R' \)**:
\[
y_{R'} = y_R = 1
\]
Thus,
\[
R' = (2a - (-11), 1) = (2a + 11, 1)
\]

To calculate the exact coordinates of \( R' \), you will need to specify the value of \( a \), the x-coordinate of the vertical line of reflection. Please provide that value, and I'll give you the exact coordinates of \( R' \).

Answer 5

To reflect point \( F \) over the vertical line \( x = -1 \), we need to know the original coordinates of point \( F \). However, since you did not provide these coordinates directly, I can show you how to find the reflected coordinates based on an assumption of what \( F \) could be, based on the options you provided.

**Reflection process**:
1. The general formula for the reflection of a point \( (x_F, y_F) \) across the vertical line \( x = -1 \) is given by:
\[
x_{F'} = 2(-1) - x_F
\]
\[
y_{F'} = y_F
\]

2. This simplifies to:
\[
x_{F'} = -2 - x_F
\]

Now, we can test the given options to see which one could be a valid reflection:

1. **Option F′(−1,4)**:
- \( x_{F'} = -1 \) which would yield \( x_F = -2 \); therefore \( F(-2, 4) \)

2. **Option F′(3,5)**:
- \( x_{F'} = 3 \) which would yield \( x_F = -8 \); therefore \( F(-8, 5) \)

3. **Option F′(5,−5)**:
- \( x_{F'} = 5 \) which would yield \( x_F = -12 \); therefore \( F(-12, -5) \)

4. **Option F′(−5,−5)**:
- \( x_{F'} = -5\) which would yield \( x_F = 2 \); therefore \( F(2, -5) \)

Now we analyze whether the original points correspond correctly to their reflected points:

- For **option F'(-1, 4)**, if \( F = (-2, 4) \), then reflecting across \( x = -1 \):
\[
x_{F'} = 2(-1) - (-2) = -2 + 2 = -1
\]
(So this option works.)

- The other options do not satisfy the condition for reflection correctly based on how they would result from reflection.

Thus, if \( F \) was originally \( (-2, 4) \), reflecting across \( x = -1 \) gives us \( F'(-1, 4) \).

### Conclusion:
The correct coordinates for \( F' \) after reflection would be **F′(−1, 4)**.