Question

In the diagram shown, line m is parallel to line n, and point p is between lines m and n.

Determine the number of ways with endpoint p that are perpendicular to line n

Answer 1

2

Explanation:

Since line m is parallel to line n, any line that is perpendicular to line n will also be perpendicular to line m. Therefore, we just need to determine the number of lines perpendicular to line n that pass through point p.

If we draw a diagram, we can see that there are two such lines: one that is perpendicular to line n and passes through the endpoint of line segment p on line m, and another that is perpendicular to line n and passes through the other endpoint of line segment p on line m. These two lines are the only ones that are perpendicular to line n and pass through point p, so the answer is 2.