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Triangle PQR is reflected over a vertical line of reflection to create triangle P'Q'R. what are the coordinates of point R'

3 answers

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 x-coordinate of the line of reflection.

Assuming the coordinates of point R are given as (x_R, y_R) and the vertical line of reflection is located at x = k, the reflection of point R will have its x-coordinate adjusted based on the distance from the line of reflection. The reflected coordinates for R', denoted as (x_R', y_R'), will be calculated as follows:

  1. Find the distance from R to the line of reflection: \(d = x_R - k\).
  2. The x-coordinate of the reflected point will be \(x_R' = k - d\) or \(x_R' = k - (x_R - k) = 2k - x_R\).
  3. The y-coordinate remains the same: \(y_R' = y_R\).

Thus, the coordinates of point R' after the reflection can be expressed as: \[ R' = (2k - x_R, y_R) \]

If you provide the specific coordinates for point R and the x-coordinate of the line of reflection, I can give you the exact coordinates for point R'.

the coordinates of point R are (-11,1)

To find the coordinates of point \( R' \) after the reflection of triangle \( PQR \) over a vertical line, we need the x-coordinate of the line of reflection.

Let’s denote the line of reflection as \( x = k \). The coordinates of point \( R \) are given as \( (-11, 1) \).

The formula for reflecting a point \( (x, y) \) over a vertical line \( x = k \) is:

\[ R' = (2k - x, y) \]

Replacing \( x \) with the x-coordinate of point \( R \): \[ R' = (2k - (-11), 1) \]

This simplifies to: \[ R' = (2k + 11, 1) \]

Now, to provide the exact coordinates, we need to know the value of \( k \). If you let me know the x-coordinate of the line of reflection, I can calculate the exact coordinates of point \( R' \).