Question

Triangle PQR is reflected over a vertical line of reflection to create Triangle P′Q′R′
. What are the coordinates of point R′
?
R=(-11,1) R'?

Answer 1

To find the coordinates of point \( R' \) after triangle \( PQR \) is reflected over a vertical line, we need to know the equation of the vertical line of reflection.

A vertical line will take the form \( x = k \), where \( k \) is a constant representing the x-coordinate of the line.

When a point \( (x, y) \) is reflected over a vertical line \( x = k \), the x-coordinate of the reflected point \( (x', y) \) is given by the formula:

\[
x' = 2k - x
\]

The y-coordinate remains the same.

Given that the coordinates of point \( R \) are \( R = (-11, 1) \), we can find the coordinates of point \( R' \) once we know the line \( x = k \).

If we assume the line of reflection is \( x = k \), we can plug in the values. For instance, if the line of reflection were \( x = 0 \):

1. The x-coordinate of \( R \) is \( -11 \).
2. Reflecting over \( x = 0 \):

\[
x' = 2(0) - (-11) = 11
\]

3. The y-coordinate remains the same, so:

\[
y' = 1
\]

Thus, the coordinates of point \( R' \) would be \( R' = (11, 1) \).

You would replace \( k \) with the actual line of reflection if it's different. If you provide the specific vertical line of reflection, I can calculate the exact coordinates for \( R' \).