The only geometric objects that can be defined using the locus of points idea are straight lines, circles, and angle bisectors.A.TrueB.False
Question
The only geometric objects that can be defined using the locus of points idea are straight lines, circles, and angle bisectors.
A. True
B. False
Solution
Analyzing the Statement
-
Understanding the Concept of Locus of Points:
- A locus is a set of points that satisfy a particular condition. It is used in geometry to define shapes and figures.
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Geometric Objects Defined by Locus of Points:
- Straight Lines: A straight line can be defined as the locus of points that are equidistant from two fixed points.
- Circles: A circle can be defined as the locus of points that are a fixed distance (radius) from a central point.
- Angle Bisectors: An angle bisector is the locus of points that are equidistant from the sides of an angle.
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Other Geometric Objects:
- Besides the mentioned figures, other geometric objects can also be defined using locus of points, such as ellipses (locus of points such that the sum of distances to two foci is constant) and parabolas (locus of points equidistant from a point and a line).
Conclusion
The statement is incorrect because it limits the locus of points to only three geometric shapes, while there are more shapes that can also be defined using the concept of a locus.
Final Answer
B. False
Similar Questions
The locus of points idea can be used to define straight lines, circles, and even more complex shapes such as parabolas.
Which geometric object is defined as the set of all points in a plane that are equidistant from two points?A.CircleB.Line segmentC.ParabolaD.Line
Which geometric objects can be defined using only two distinct points, A and B? Select all that apply.
Which geometric object is defined as the set of all points in a plane that are equidistant from the two sides of a given angle?
The locus of points idea allows you to define a circle without giving a numerical value for the radius.
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