Draw and describe the locus of points in the plane that are equidistant from parallel lines l and m.

Q: Determine whether the statement " If two lines L1 and L2 are each parallel to a plane, then L1 and…

A: Two lines  L1 and L2 can be perpendicular to each other and be parallel to the same plane at the…

Q: Describe a method for determining whether four points P, Q , R , and S lie in the same plane?

A: We will show a method for determining whether four points P,Q,R and S lie in the same plane.

Q: Any two lines in space are either intersecting or parallel.

A: Given statement is  ' Any two lines in space are either intersecting or parallel' . The statement is…

Q: 5. Construct a copy of the line segment below. U V

A: To construct a linesegment by copying using a compass

Q: Describe the locus of points in space that are at a distance of 3cm from point P

A:

Q: Select from the drop-down menus to correctly complete each sentence. The set of all points In a…

A: Given:           We have to find the definitions below.

Q: Find the coordinates of the midpoint of the line segment PQ. P(x-Z, r), Q(x + z, r) Select one: O A.…

A: The mid-point formula of a line segment is, x,y=x1+x22,y1+y22 where x,y is mid-point of the line…

Q: Determine whether the statement " Two lines in space are either intersecting or parallel", is true…

A:

Q: Which of the following terms is defined as "the set of all points in a plane that are a fixed…

A: A circle is the set of all points in a plane that are a fixed distance from a given point. The…

Q: Construct a line perpendicular to the line given through the point P at the right.

A: To plot the line perpendicular to the given line through the point P

Q: Postulate 12 states that if two points lie in a plane, the line that contains them lies in the…

A: We need to determine whether the given statement is true or false. Postulate 12 states that if two…

Q: A Draw and describe the locus of points in the plane that are equidistant from the sides of ZABC. C

A: Definition: The locus of points in a plane and equidistant from the sides of an angle is the angle…

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: There are infinitely many secant lines from an exterior point to a circle. True or False? O True…

A: From a point outside the circle, infinite secants can be drawn to the circle

Q: Show that the line containing the points(a,b) and (b,a) , a ≠b is perpendicular to the line…

A: The objective is to show that the line containing the points a,b and b,a , a≠b is perpendicular to…

Q: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: ind the locus of points equidistant from two parallel planes.

A: To Find the locus of points equidistant from two parallel planes.

Q: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: What is the locus of points in space equidistant from two parallel planes?

A: Locus: If the two lines are in Rn the points equidistant from them form an n−1 dimensional…

Q: In the figure, which of the points A, B, C, D, and E belong to “the locus of points in the plane…

A: Consider the given figure, The locus of points in the plane that are at distance r from the point P…

Q: Sketch the locus of points P(x, y) and write down its Cartesian equation given that P is equidistant…

A:

Q: Which point is one fourth of the way between point A and point Bon the line segment AB shown on the…

A:

Q: construct a line that goes through point A and is perpendicular to a line.

A:

Q: There are infinitely many secant lines from an exterior point to a circle. True or False? O True O…

A:

Q: Prove that a line cannot contain three distinct points.

A: We prove that a line cannot contain three distinct points by method of contradiction.

Q: Consider any eight points such that no three are collinear.How many lines are determined?

A: Given :                         There are 8 points    To find :                      To…

Q: Prove that there exists a set of two lines containing all the points of the geometry.

A:

Q: In a plane, what is the locus of points equidistant from two given points?a. a point b. a circle c.…

A: Query- In a plane, what is the locus of points equidistant from two given points? Answer- A point is…

Q: Show that the line joining the points P(0,1, 2) and Q(3, 4, 8) is parallel to the line joining the…

A: From the given problem:    L1:P0,1,2→x1,y1,z1Q3,4,8→x2,y2,z2   L2:R-2,32,-3→x1,y1,z1S52,6,6→x2,y2,z2…

Q: Sketch the locus of points equidistant from D and E is the perpendicular bisector of line DE

A: Consider the line DE which is obtained by joining two point D and E. To sketch the locus of points,…

Q: For Fano's geometry, prove that the lines through any one point of the geometry contain all the…

A: Given detail: For Fano's geometry, prove that the lines through any one point of the geometry…

Q: Let A, B, C be three collinear points and let P be a point outside the line through A, B, C. Using…

A: Sketch the diagrams with the help of geometrical tools and the hint given in the question.

Q: find the locus of a moving point which forms a triangle of area 21 square units with the point…

A:

Q: Determine the midpoint that lies between the two given points. (3π, 3) and (6π, 9)

A:

Q: If a slide, a tetherball, and a swing are all 20 feet apart in a park, where could a water fountain…

A:

Q: Prove that parallel lines determine only one plane.

A:

Q: Prove that the line joining the midpoint of a median to a vertex of the triangle trisects the side…

A: Here ask to prove the line joining the midpoint of a median to a vertex of the triangle trisectsthe…

Q: Describe a method for determining whether four points P , Q , R , and S , lie in the same plane

A: We know that if some points lie on the same plane, then their slope would be same.

Q: Give the Cartesian equation of the locus of points P(x, y) given that P is 5 units from the point…

A: Any point on the Cartesian plane is represented as x, y. The locus is a set of points on the…

Q: Find the coordinates of the midpoint of the line (a, 1), (1, a)

A:

Q: . In a plane, what is the locus of points equidistant from the sides of a square?a. a square b. a…

A: To find: The locus of points equidistant from the sides of a square in a plane.

Q: Let A be the point with coordinates (0, -3, 3) and let B be the point with coordinates (2, 0, 0).…

A: Given: A=0,-3,3B=2,0,0

Q: Show that the following sets of points are collinear and find the equation of line…

A: Three or more points are collinear, if slope of any two pairs of points is same. With three points…

Q: hat are the coordinates of the point on the directed line segment from (–7,5) t ',-9) that…

A: In the question we need to find the coordinates of a point which divides the line segment joining…

Q: Find the locus of the points that are equidistant to the point F (0,2) and the line y=-2

A: Use distant formula..

Q: Give the location of Rome as an ordered pair (x, y).

A: Given plot is, We need to find the co-ordinates of x and y for Rome from the given plot.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.