Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3  are perpindicular.

Q: Determine which of the points (-5,5), (2, −2), and (−2,−1) lie on both the lines x₁ + 4x2 = = -6 and…

A:

Q: Show that the three points (4, 2), (7, 5), (9, 4) lie on a right line.

A: Given points   Let A (4,2) , B (7,5) , C (9,4)

Q: Find the point on the line 3x + 6y +2=0 which is closest to the point (2,-2). Answer is

A: Foot of perpendicular

Q: The points (x, -5) and (2, y) are on the line containing the points (-14, 7) and (10, 1). What is…

A: equation of line containing two points (x1,x2) and (y1,y2) is y-y1=y2-y1x2-x1x-x1

Q: the y-intercept of (-7,-4) and (-5,-6

A: Given line passes through the points (-7,-4) and (-5,-6)

Q: Lesson 10 Practice Problems 1. Select all equations that are parallel to the line 2x + 5y = 8.…

A: solve the Ans is:

Q: Determine the equation of the line L which passes through the points A = (8, 11) and B = (12, 17)

A:

Q: The line perpendicular to y=9x+5 and containing (5,4)

A: Given:

Q: Determine which of the points (4, -1), (1, -5), and (-2,2) lie on both the lines ₁ + 2x2 = 2 and 4x₁…

A:

Q: Determine B such that the line 3x+2y-7=0 is perpendicular to 2x-By+2=0.

A:

Q: Which of the following is the point of intersection between the lines 3x + y = 10  and  2x - y = 5…

A: Two given equations of lines are: 3x+y=10 and 2x-y=5 First we need to solve this system of…

Q: Determine the x and y intercept of the line y+6=-5(x+1)

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.