Problem 2 Using a Perpendicular Bisector
A park director wants to build a T-shirt stand equidistant from the Rollin' Coaster and the Spaceship Shoot. What are the possible locations of the stand? Explain.
Plan
How do you find points that are equidistant from two given points?
By the Converse of the Perpendicular Bisector Theorem, points equidistant from two given points are on the perpendicular bisector of the segment that joins the two points.
To be equidistant from the two rides, the stand should be on the perpendicular bisector of the segment connecting the rides. Find the midpoint A of
✓ Got It?
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- Suppose the director wants the T-shirt stand to be equidistant from the paddle boats and the Spaceship Shoot. What are the possible locations?
- Reasoning Can you place the T-shirt stand so that it is equidistant from the paddle boats, the Spaceship Shoot, and the Rollin' Coaster? Explain.
Essential Understanding There is a special relationship between the points on the bisector of an angle and the sides of the angle.
The distance from a point to a line is the length of the perpendicular segment from the point to the line. This distance is also the length of the shortest segment from the point to the line. You will prove this in Lesson 5-6. In the figure below, the distances from A to l and from B to l are represented by the red segments.
In the diagram,
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs