https://file.aiquickdraw.com/mathbot/file/1726104102439csgtxpv9.jpg

Let's solve the problems visible in the image:

### Problem 1 (Top Left):
**Trapezoid QRST** with vertices \( Q(4, -1), R(6, -1), S(8, -6), T(2, -6) \) is reflected over the line \( x = -1 \). What is the location of \( T' \)?

To reflect a point across the vertical line \( x = -1 \), the formula is:
\[
x' = 2(-1) - x
\]
For point \( T(2, -6) \):
- Apply the formula to the \( x \)-coordinate: 
\[
x' = 2(-1) - 2 = -2 - 2 = -4
\]
- The \( y \)-coordinate remains the same.

Thus, \( T'( -4, -6 ) \).

### Problem 2 (Top Right):
**Parallelogram STUV** with vertices \( S(-3, 4), T(-1, 7), U(5, 7), V(3, 4) \) is reflected over the line \( y = -x \). What is the location of \( T' \)?

When reflecting a point

Solve the problems related to reflections involving a trapezoid and a parallelogram as given in the provided image.

Explore how to solve reflection problems involving a trapezoid and a parallelogram in coordinate geometry. This includes key formulas and transformations, suitable for students in Grades 8-10.

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