In the given image, we are working with a rectangular prism (box-like figure), and we need to find the line that is perpendicular to line QP.

Looking closely at the points and lines, the line QP lies on the face of the prism formed by points Q, U, V, P (the base face). To identify a line perpendicular to QP, we should look for a line that forms a right angle with QP.

From the image, we observe that:

• Line QP lies horizontally on the base.
• The vertical lines in the prism, such as QT and QU, are perpendicular to lines in the base face.

Thus, the line QT is perpendicular to line QP, because QT is a vertical line and QP is a horizontal line, forming a right angle at point Q.

Answer:

The line QT is perpendicular to line QP.

Would you like more details or have any other questions?

Here are 5 related questions you might want to explore:

1. What is the relationship between line QT and other lines such as QR or QS?
2. Can we identify any other lines perpendicular to QP besides QT?
3. What are the parallel lines to QP in the prism?
4. How would you calculate the length of line QT if the dimensions of the prism were given?
5. How can we determine which lines are skew in this figure?

Tip: To determine perpendicularity in 3D shapes, always look for lines that form right angles and belong to different planes, such as vertical versus horizontal lines.