Find the value of X such that <19,7> and <4,X> are perpendicular

Q: 8. Determine whether the lines L,and L2 are parallel, skew or intersecting. If they intersect find…

A: Given data: The expression for the first line is L1: x=3+2t, y=4-t, z=1+3t. The expression for the…

Q: A, B, and C are three points on a line. AC = 8, ВС %3 4, and AB = 12. Which point must be between…

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Q: Find the distance between the points P = (1, 3) and Q = ( - 4, 2).

A: We have to find the distance between point P(1,3) and Q(-4,2)

Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: MO and PR are parallel lines.

A:

Q: Are the lines parallel, perpendicular or neither. Show work. 4 ソ=ーx+2 3. 3x+4y = 4 %3D %3D

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Q: Show that the equation x+y+z=4 ,2x+5y-2z=3,x+7y-7z=5 are not consistent

A: A square system of equations represented by, AX=B is considered inconsistent if the inverse of the…

Q: Find the value of z that makes lines u and v parallel. 6x-3 117 O -5

A: We know that when two lines are crossed by another line (called the Transversal), the pairs of…

Q: Given (x,4) and (-3,y), find x and y such that the midpoint between these two points is (6,4).

A: To find the x and y such that mid point of (x,4) and (-3,y) is (6,4)

Q: Given (x, 5) and (-9, y), find x and y such that the midpoint between these two points is (4, 3).

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Q: All lines are either parallel or perpendicular. O True O False

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Q: 11a) Are the two lines parallel? Show work 4 (3, 2) -30] 2. (5,-1) 【け1.-B12 2

A: Given: Co-ordinates of line l1=(-3,0) and (3,2) Co-ordinates of line l2=(-1,-3) and (5,-1)

Q: What value of x would prove that lines /and m are parallel? (5x + 3) (9x-33)

A: For lines l and m to be parallel, The sum of internal angles made by intersecting line is 180°.

Q: 9) 7x+4 60° 1.

A: The figure is given by To evaluate: The value of x

Q: Determine whether the lines h and I, intersect, are parallel, or are skew. 1: n= 4i+3j+ (i-j+6k) 12:…

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Q: Show that the lines 2 x+3 y-1 and 6 x-12 y-1=0 are not perpendicular

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Q: What value of x would prove that lines /and m are parallel?

A: Given that lines m and l are parallel.

Q: 4. In this figure, lines a and b are intersected by line t.

A: Answer: ∠1 ≅∠3  .

Q: and

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Q: Find the value of x that makes lines u and v parallel. 8) 9) x+ 62 7x+4 125° 60

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Q: Find the value of x that makes lines a and b parallel 19x-4 a 110° O 6 O 5 O 7 О 1

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Q: Find the value of a that makes lines u and v parallel. 125 + x x+65 O -5 O 12

A: Solution

Q: Let point A = (m,n) and point B = (x,y). If A and B lie in one horizontal line and B is to the right…

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Q: 25. Determine if the segments AB and BC are parallel, perpendicular o neither. (Find the slopes.)*…

A: If two lines have same slope, then they are said to be parallel. These lines are perpendicular if…

Q: Find the value of a that makes lines u and v parallel. 130° x+ 135 y O 5

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Q: Prove that for each point the are at least two straight lines that pass through it, accordir to the…

A: There is a point and we have to show that 2 or more lines can pass from that point.

Q: Consider à = (2,1,k), and b = (k,-8,k). Find the value of k such that å and bare perpendicular.

A: We can find the values of k as below.

Q: Determine whether the lines L1: (−2, −1) and L2: (1, 3), (5, −5) passing through the pairs of points…

A: Since, we have been given that two lines are L1: (-2,-1), (1,5) and L2: (1,3) , (5,-5). Our Aim is…

Q: Prove that all the points on a perpendicular bisector of a line segment AB are equidistant from the…

A: Statement:All the points on a perpendicular bisector of a line segment AB are equidistant from the…

Q: How to find the value of x that makes m and n parallel

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Q: Find the relationship between x and y such that the point (x,y) is equidistance from the points…

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

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Q: Consider the figure, where transversals s and intersect parallel lines m and n 51 and 72 What is the…

A: Opposite angles a intersecting lines are equal. Sum of angles in a triangle is 180 degrees.

Q: Find the relation between x and y such that the point (x,y) is equidistant from the points (7,1) and…

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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: r, m and n be the direction cosines of the line L. Show that r2 + m2 + n2 = 1.

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Q: State whether the lines are parallel, perpendicular, the same (coincident), or none of these. 2x +…

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Q: Indicate whether the statement is true or false. If coplanar lines r and s are cut by transversal t…

A: True

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: Find k so that the line through (3, 2) and (k, 3) is a. parallel to 25x + 17y = 34, b. perpendicular…

A: We will be using the following concepts: Parallel lines have the same slope. The product of slope…

Q: Prove that, if two lines are parallel to a third line, then the lines are parallel to each other

A: Consider the following figure.

Q: 1 2 Show that 1 and 3 are perpendicular. -1

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Q: A line is perpendicular to another line, if and only if

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Q: Use the given information to decide which lines are parallel. Justify your answers with a theorem or…

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Q: Find b so that the points (4,-6), (5,-8), and (b,-2) lie on the line

A: Please find the solution in the attached images :

Q: Suppose a line that appears parallel to side BC of △ABC intersects sides AB and AC at points X and Y…

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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.

Q: 4) Which of the following pairs of points define a line segment parallel to the x-axis? O(4,3)(-4,3)…

A: We have to identify the line segment parallel to x axis.

Q: Given ∡ 2 + ∡ 3 = 180°∡ 2 + ∡ 3 = 180°, which theorem proves the lines r and s parallel.

A: If two parallel lines are cut by a transversal, then same side interior angles are supplementary.…

Q: Find the product of the lengths of the perpendiculars drawn from (2,1) upon the lines…

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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.