An ice cream vendor wants to be located equidistant from the entrances of a zoo and an amusement park. Should he locate his stand on a perpendicular bisector, an angle bisector, a median, or an altitude? O A. perpendicular bisector B. angle bisector C. median altitude

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Question 16

## Geometric Principles in Practical Situations

An ice cream vendor wants to be located equidistant from the entrances of a zoo and an amusement park. Should he locate his stand on a perpendicular bisector, an angle bisector, a median, or an altitude?

### Options:
- **A. Perpendicular bisector**
- **B. Angle bisector**
- **C. Median**
- **D. Altitude**

In this scenario, understanding fundamental geometric principles can assist in locating the most optimal point for the ice cream stand. The vendor aims to be equidistant from two specific points: the entrance of the zoo and the entrance of the amusement park. 

**Discussion:**

- **Perpendicular Bisector**: A perpendicular bisector is a line segment that divides another line segment into two equal parts at a 90-degree angle. When locating a point that is equidistant from two points, the perpendicular bisector of the segment joining these two points is the appropriate choice.

- **Angle Bisector**: An angle bisector divides an angle into two equal angles. It doesn't necessarily provide the property of equidistance between two separate points unless these points are vertices of an angle.

- **Median**: A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. This also does not guarantee equal distance from two distinct points unless they form part of a triangle.

- **Altitude**: An altitude of a triangle is a perpendicular dropped from a vertex to the line containing the opposite side. This similarly does not satisfy the condition of being equidistant from two distinct points on its own.

**Conclusion:**

To achieve the goal of being equidistant from the entrances of both a zoo and an amusement park, the vendor should locate his stand on the perpendicular bisector of the segment joining the two entrances.

**Answer:**
- **A. Perpendicular bisector**
Transcribed Image Text:## Geometric Principles in Practical Situations An ice cream vendor wants to be located equidistant from the entrances of a zoo and an amusement park. Should he locate his stand on a perpendicular bisector, an angle bisector, a median, or an altitude? ### Options: - **A. Perpendicular bisector** - **B. Angle bisector** - **C. Median** - **D. Altitude** In this scenario, understanding fundamental geometric principles can assist in locating the most optimal point for the ice cream stand. The vendor aims to be equidistant from two specific points: the entrance of the zoo and the entrance of the amusement park. **Discussion:** - **Perpendicular Bisector**: A perpendicular bisector is a line segment that divides another line segment into two equal parts at a 90-degree angle. When locating a point that is equidistant from two points, the perpendicular bisector of the segment joining these two points is the appropriate choice. - **Angle Bisector**: An angle bisector divides an angle into two equal angles. It doesn't necessarily provide the property of equidistance between two separate points unless these points are vertices of an angle. - **Median**: A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. This also does not guarantee equal distance from two distinct points unless they form part of a triangle. - **Altitude**: An altitude of a triangle is a perpendicular dropped from a vertex to the line containing the opposite side. This similarly does not satisfy the condition of being equidistant from two distinct points on its own. **Conclusion:** To achieve the goal of being equidistant from the entrances of both a zoo and an amusement park, the vendor should locate his stand on the perpendicular bisector of the segment joining the two entrances. **Answer:** - **A. Perpendicular bisector**
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