Question

Use the coordinates to answer the question.
Triangle PQR:
Point P: (-8, 9)
Point Q: (-12, 7)
Point R: (-11, 1)

Triangle P'Q'R':
Point P': (-6, 9)

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

Answer 1

To find the coordinates of point R' after reflecting triangle PQR over a vertical line of reflection, we first need to determine the vertical line of reflection.

We have the original coordinates for point R: R = (-11, 1) and the new coordinates for point P': P' = (-6, 9). Since P' is the reflection of P over the vertical line of reflection, we can identify the line of reflection by finding the midpoint between P and P'.

The coordinates of point P are (-8, 9) and point P' is (-6, 9). The x-coordinates of these points are -8 and -6. We can find the midpoint's x-coordinate, which will help us to find the line of reflection:

Midpoint's x-coordinate:

\[
\frac{-8 + (-6)}{2} = \frac{-14}{2} = -7
\]

Thus, the vertical line of reflection is the line \( x = -7 \).

Now that we have the line of reflection, we can reflect point R = (-11, 1) over the line \( x = -7 \).

To find the reflected point R', we calculate the distance from R to the line \( x = -7 \):

\[
\text{Distance from } R \text{ to the line } x = -7 = -11 - (-7) = -11 + 7 = -4
\]

Since we are reflecting, we move 4 units to the right from -7:

\[
-7 + 4 = -3
\]

Thus, the coordinates of R' after reflection are:

\[
R' = (-3, 1)
\]

So the coordinates of point R' are (-3, 1).