Are the lines Perpendicular? Explain.(est review) 4 (4, 3) (-4, 2) 2 4. -2 (-5, –3) ▼ (0, -4) 2.

Q: Find the point (x₁,x₂) that lies on the line x₁ + 3x₂ = 10 and on the line x₁ - x₂ = -2. See the…

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Q: y 14 12 10 8 6 (2,5) (8,13) What is the equation of a line parallel to the one shown above?

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Q: 215- Find the Line that passes throug h the point (1,2) and through the point of inter Section of…

A: Given the line passes through the point (1,2) and point of intersection of lines x+2y=3 2x-3y=-1

Q: In Exercises 23-30, find the distance between the two points. (See Example 4.) 23. A(13, 2) and B(7,…

A: For distance between (a,b) and (p,q)distance, d = (a-p)2+(b-q)223) A(13,2) and B(7,10)      AB= d =…

Q: 22. Write the equation of the line.

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Q: Identify the x and y intercepts. (See attachment).

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Q: 2. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 1) and K(10, 7). (8,…

A: To calculate the mid point of join of given points. To find the slope of the line perpendicular to…

Q: Find the point on the line 2x + y = 5 that is closest to the point (-4, 3). (x, v) = (

A: We haveThe line 2x+y=5 closest to the point −4,3

Q: Plot the following six points: (- 2, 2) (1, 5) (– 5, – 1) (1, 0) (4, - 4) (0, – 3)

A: The direction on the graph of x-axis and y-axis is given below. The origin is (0,0). The horizontal…

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.