Question about Point, Line, and Plane
Subject Mathematics
Mathematics
Source Originais Teachy
Originais Teachy
Topic Point, Line, and Plane
Point, Line, and Plane
Difficulty Very Hard
Very Hard
(Originais Teachy 2023) - Question Very Hard of Mathematics
Consider a point P in the plane that does not belong to a line r. Let S be the set of all points in the plane that are symmetric to P with respect to r. Prove that S is a line and determine its position relative to r. Furthermore, prove that for any point Q belonging to S, the line passing through Q and parallel to r contains exactly one point of intersection with r.Answer sheet:
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur id consequat justo. Cras pellentesque urna ante, eget gravida quam pretium ut. Praesent aliquam nibh faucibus ligula placerat, eget pulvinar velit gravida. Nam sollicitudin pretium elit a feugiat. Vestibulum pharetra, sem quis tempor volutpat, magna diam tincidunt enim, in ullamcorper tellus nibh vitae turpis. In egestas convallis ultrices. Sed non sem ultricies, sollicitudin sem facilisis, commodo justo. Maecenas mattis sodales nunc, et auctor massa fermentum a. Maecenas eget nisl felis.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur id consequat justo. Cras pellentesque urna ante, eget gravida quam pretium ut. Praesent aliquam nibh faucibus ligula placerat, eget pulvinar velit gravida. Nam sollicitudin pretium elit a feugiat. Vestibulum pharetra, sem quis tempor volutpat, magna diam tincidunt enim, in ullamcorper tellus nibh vitae turpis. In egestas convallis ultrices.
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