Interior vs Exterior Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyA triangle is drawn on paper. Point is inside the triangle and point is outside. If you draw a straight line from to , how many times must it cross the boundary of the triangle?
Solution
- 1 Step 1: Visualize a path from an interior point to an exterior point . To travel from inside to outside, you must pass through the boundary at least once.
- 2 Step 2: For a convex shape like a triangle, a straight line segment from an interior point to an exterior point crosses the boundary exactly once.
Answer
Exactly once.
This is a fundamental property of boundaries: any path connecting an interior point to an exterior point must cross the boundary at least once. For a convex shape and a straight-line path, it crosses exactly once. This idea is central to understanding what a boundary separates.
About Interior vs Exterior
Interior consists of points strictly inside a boundary; exterior consists of points strictly outside the boundary.
Learn more about Interior vs Exterior →More Interior vs Exterior Examples
Example 1 easy
A circle is drawn on a piece of paper. Point [formula] is 3 cm from the center and the radius is 5 c
Example 2 mediumA rectangle has vertices at [formula], [formula], [formula], and [formula]. Determine whether the po
Example 4 hardA point [formula] and a circle centered at [formula] with radius [formula]. Is [formula] interior or