Quadrilateral ABCD is reflected in edge BC. How many of the vertices are invariant?
Understand the Problem
The question is asking how many vertices of the quadrilateral ABCD remain unchanged after it is reflected across the edge BC. To solve this, we need to consider the properties of symmetry and reflection in geometry.
Answer
2
Answer for screen readers
The number of invariant vertices is $2$.
Steps to Solve
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Identify the line of reflection The line of reflection is edge BC, which means we will reflect the quadrilateral across this line.
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Determine the positions of vertices Label the vertices of the quadrilateral as A, B, C, and D. Since we are reflecting across edge BC, we will assess the positions of each vertex relative to this line.
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Analyze the vertices for invariance The vertices A and D are not on the line BC, so they will change position after reflection.
Vertices B and C are located on edge BC, making them invariant because points on the line of reflection do not move. -
Count the invariant vertices Now, we can count the number of invariant vertices. Vertices B and C remain in place, while A and D do not.
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Final count The final count of invariant vertices is (2), corresponding to vertices B and C.
The number of invariant vertices is $2$.
More Information
In geometry, a reflection across a line keeps points on that line unchanged while reversing the positions of other points. This property helps determine which vertices stay in their original positions.
Tips
Reflecting all vertices instead of recognizing the line of reflection might lead to incorrect conclusions about which vertices are invariant. Always check the position of each vertex relative to the line of reflection.
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