Locus
ICSE · Class 10 · Mathematics
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The locus of a point that is always 5 cm away from a fixed point O is a circle. What is the radius of this circle?
Points A and B are 8 cm apart. Find the distance from point A to any point on the perpendicular bisector of segment AB.
Two parallel lines are 6 cm apart. What is the distance between each parallel line and their locus of points equidistant from both?
A point P moves such that its distance from point A(2,3) is always 4 units. The equation of this locus is:
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Which of the following represent valid loci? (Select all correct answers)
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Circle with center at origin and radius 3, Perpendicular bisector of a line segment, Angle bisector of two intersecting lines, A single point
A locus is the set of all points satisfying a given condition. A circle, perpendicular bisector, angle bisector, and even a single point can all be loci depending on the conditions. However, the entire plane cannot be a locus as it doesn't satisfy any specific geometric condition.
In triangle ABC, the locus of points equidistant from sides AB and AC is:
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The angle bisector of angle A
The locus of points equidistant from two intersecting lines (sides AB and AC) is the angle bisector. Since AB and AC intersect at vertex A, the angle bisector of angle A contains all points equidistant from these two sides.
The perpendicular distance from any point on the locus to two given points is always equal.
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True
This statement is true for the perpendicular bisector locus. By definition, the perpendicular bisector of a line segment is the locus of all points equidistant from the endpoints. Every point on this locus has equal distance to both given points.
A wheel of radius 10 cm rolls on a straight road. The locus of the center of the wheel is a line parallel to the road at distance:
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10 cm
When a wheel rolls on a straight road, its center maintains a constant distance from the road equal to the radius of the wheel. Since the wheel has radius 10 cm, the center's locus is a line parallel to the road at distance 10 cm above it.
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