prove that if A is a point on the perpendicular bisector of line segment B-C  then A is the same distance from point B as it is from point C. Conversely, show that if point A is the same distance from point B as it is from point C, then A must be a point on the perpendicular bisector of line segment BC

Q: Verify that the points (7, 12) and (11, 18) divide the line segment joining (3, 6) and (15, 24) into…

A: Given points are x1,y1=3,6x2,y2=7,12x3,y3=11,18x4,y4=15,24

Q: the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axes at concyclic points,then prove that…

A:

Q: Show that the midpoint of the line segment joining the points (a, b) and (c,d) is ((a + c)/2, (b +…

A: Mid point formula is:

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: What two points can be drawn between a line segment?

A: Yes two point can be drawn between lime segment

Q: Show that the lines 2x+3y-2=0, 3x-2y+23=0 and x-5y+12=0 are the sides of an isosceles triangle. Find…

A: Plot the given 3 st. lines and mark the intersection points forming the triangle.

Q: Determíne the length of the common perpendícular dístance between two línes in space, the first líne…

A: Given First line passing through point A24,0,0 and B0,8,12and the second line passing through point…

Q: how that the lines x- 7y – 22 =0, 3x+4y +9 = 0 and 7x + y – 54 = 0 form a right angled osceles…

A:

Q: a and b are two points in the third-dimenson. Show the equation that describes the set of points…

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.