Which points are on the perpendicular bisector of the given segment? Check all that apply.
(-8,19)
(1,-8)
(0,19)
(-5,10)
(2,-7)
Answer (2)
The problem is ill-posed because the segment is not defined, making it impossible to determine the perpendicular bisector and identify points on it.
Explanation
Problem Analysis The problem asks us to identify points on the perpendicular bisector of a segment. However, the segment itself is not defined. Without knowing the endpoints of the segment, we cannot determine its midpoint or the slope of the perpendicular bisector. Therefore, we cannot determine which of the given points lie on the perpendicular bisector.
Reasoning Since the segment is not defined, it is impossible to determine the perpendicular bisector and therefore impossible to determine which of the given points lie on it. The problem is ill-posed because the segment is not defined.
Examples
In city planning, understanding perpendicular bisectors is crucial when designing roads or infrastructure that need to be equidistant from two key locations, such as hospitals or schools. For example, if you want to build a new bus stop that is equally accessible to two residential areas, you would locate it on the perpendicular bisector of the line segment connecting the centers of those areas. This ensures fair access and optimal service for both communities.
To identify points on the perpendicular bisector of a segment, we need the endpoints of the segment. As the segment's endpoints are not provided, we cannot perform the necessary calculations to determine which points are on the bisector. Thus, we cannot conclude any of the given points lie on it.
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