Locus of a Point Equidistant from Two Fixed Points

Q.

With $\mathrm{PQ}$ of length $6.1\mathrm{cm}$ as diameter, draw a circle.

Q.

Construct a triangle ABC with AB = 6 cm, AC = BC = 9 cm. Then there exists a point which is 4 cm from A and equidistant from B and C, on the perpendicular bisector of the line BC.

1. False

2. True

Q.

In the given triangle ABC, the point of intersection of the locus of a point equidistant from AB and AC and the locus of a point equidistant from B and C lies inside the triangle.

1. False

2. True

Q.

Draw a circle of radius 5 cm and mark two chords AB and AC of the circle of lengths 6 cm and 4 cm respectively, using ruler and compasses only. Then the point of intersection of locus of points, inside the circle, that are equidistant from A and C and the locus of points, inside the circle, that are equidistant from A and B, is the centre of the circle.

1. True

2. False

Q.

On a graph paper plot the points A(-4, 2), B(2, -6) and C(1, 7). Then the point of intersection of the locus of a point equidistant from B and C and the locus of a point equidistant from A and C lies in the fourth quadrant.

1. True

2. False

Q.

Name the locus of a point which is equidistant from two fixed points.

1. The bisector of the line segment joining these two points

2. The perpendicular bisector of the line segment joining these two points

3. A line parallel to the line segment joining these two points

4. A circle whose diameter is the line segment joining these two points

Q.

Use a graph paper for this question. Take 1 cm = 1 unit on both the axes.

Plot the points A(2, 2), B(6, 4) and C(3, 8). Construct the locus of points equidistant from A and B. Also, construct the locus of points equidistant from AB and AC. Locate the point P such that PA = PB and P is equidistant from AB and AC. Then the length of PA in cm is

1. 2

2. 2.5

3. 3

4. 2.6

Q.

The locus of vertices of all isosceles triangles having a common base is

1. a line parallel to the common base of the triangle

2. a line parallel to the common base of the triangle which is 1 cm away from it

3. the perpendicular bisector of the common base of the triangles

4. the bisector of the common base of the triangles