In Exercises 11 to 22, sketch and describe each locus in the plane. Given that congruent

In the figure, which of the points A, B, C, D, and E belong to the locus of points in the plane that are at distance r from point P?

In the figure, which of the points F, G, H, J, and K belong to the locus of points in the plane that are at distance r from line ?

In Exercises 3 to 8, use the drawing provided. Given: Obtuse Construct: The bisector of

In Exercises 3 to 8, use the drawing provided. Given: Obtuse Construct: The bisector of

In Exercises 3 to 8, use the drawing provided. Given: Obtuse Construct: The perpendicular bisector of

In Exercises 3 to 8, use the drawing provided. Given: Obtuse Construct: The perpendicular bisector o

In Exercises 3 to 8, use the drawing provided. Given: Obtuse Construct: The altitude from A to (HINT: Extend .)

In Exercises 3 to 8, use the drawing provided. Given: Obtuse Construct: The altitude from B to

Given: Right Construct: The median from S to

Given: Right Construct: The median from R to

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of points that are at a given distance from a fixed line.

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of points that are equidistant from two given parallel lines.

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of points that are at a distance of 3 in. from a fixed point O.

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of points that are equidistant from two fixed points A and B.

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of points that are equidistant from three noncollinear points D, E, and F.

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of the midpoints of the radii of a circle O that has a radius of length 8 cm.

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of the midpoints of all chords of circle Q that are parallel to diameter

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of points in the interior of a right triangle with sides of 6 in., 8 in., and 10 in. and at a distance of 1 in. from the triangle.

In Exercises 11 to 22, sketch and describe each locus in the plane. Find the locus of points that are equidistant from two given intersecting lines.

In Exercises 11 to 22, sketch and describe each locus in the plane. Given that congruent circles O and P have radii of length 4 in. and that the line of centers has length 6 in., find the locus of points that are 1 in. from each circle.

In Exercises 11 to 22, sketch and describe each locus in the plane. For Exercises 21 to 26, use the grid and your compass (as needed) to locate several points on the parabola having the given focus F and directrix d. Then sketch the parabola that is characterized by these points.

In Exercises 11 to 22, sketch and describe each locus in the plane. For Exercises 21 to 26, use the grid and your compass (as needed) to locate several points on the parabola having the given focus F and directrix d. Then sketch the parabola that is characterized by these points.

For Exercises 21 to 26, use the grid and your compass (as needed) to locate several points on the parabola having the given focus F and directrix d. Then sketch the parabola that is characterized by these points.

For Exercises 21 to 26, use the grid and your compass (as needed) to locate several points on the parabola having the given focus F and directrix d. Then sketch the parabola that is characterized by these points.

For Exercises 21 to 26, use the grid and your compass (as needed) to locate several points on the parabola having the given focus F and directrix d. Then sketch the parabola that is characterized by these points.

For Exercises 21 to 26, use the grid and your compass (as needed) to locate several points on the parabola having the given focus F and directrix d. Then sketch the parabola that is characterized by these points.

In Exercises 27 to 34, sketch and describe the locus of points in space. Find the locus of points that are at a given distance from a fixed line.

In Exercises 27 to 34, sketch and describe the locus of points in space. Find the locus of points that are equidistant from two fixed points.

In Exercises 27 to 34, sketch and describe the locus of points in space. Find the locus of points that are at a distance of 2 cm from a sphere whose radius is 5 cm.

In Exercises 27 to 34, sketch and describe the locus of points in space. Find the locus of points that are at a given distance from a given plane.

In Exercises 27 to 34, sketch and describe the locus of points in space. Find the locus of points that are the midpoints of the radii of a sphere whose center is point O and whose radius has a length of 5 m.

In Exercises 27 to 34, sketch and describe the locus of points in space. Find the locus of points that are equidistant from three noncollinear points D, E, and F.

In Exercises 27 to 34, sketch and describe the locus of points in space. In a room, find the locus of points that are equidistant from the parallel ceiling and floor, which are 8 ft apart.

In Exercises 27 to 34, sketch and describe the locus of points in space. Find the locus of points that are equidistant from all points on the surface of a sphere with center point Q.

In Exercises 35 and 36, use the method of proof of Theorem 7.1.1 to justify each construction method. The perpendicular bisector method.

In Exercises 35 and 36, use the method of proof of Theorem 7.1.1 to justify each construction method. The construction of a perpendicular to a line from a point not on the line.

In Exercises 37 to 40, refer to the line segments shown. Construct an isosceles right triangle that has hypotenuse .

In Exercises 37 to 40, refer to the line segments shown. Construct a rhombus whose sides are equal in length to AB and one diagonal of the rhombus has length CD.

In Exercises 37 to 40, refer to the line segments shown. Construct an isosceles triangle in which each leg has length CD and the altitude to the base has length AB.

In Exercises 37 to 40, refer to the line segments shown. Construct an equilateral triangle in which the altitude to any side has length AB.

Construct the three angle bisectors and then the inscribed circle for obtuse .

Construct the three perpendicular bisectors of sides and then the circumscribed circle for obtuse .

Use the following theorem to locate the center of the circle of which is a part. Theorem: The perpendicular bisector of a chord passes through the center of a circle.

Use the following theorem to construct the geometric mean of the numerical lengths of the segments and . Theorem: The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.

Use the following theorem to construct a triangle similar to the given triangle but with sides that are twice the length of those of the given triangle. Theorem: If the lengths of the three pairs of sides for two triangles are in proportion, then those triangles are similar

Verify this locus theorem: The locus of points equidistant from two fixed points is the perpendicular bisector of the line segment joining those points.