. For the figure to Indicate how yo theorems and/c The parallel line Justifications:

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: Prove that for any two points A and B, line segment AB = line segment BA

A: To prove that for any two points A and B, line segment AB = line segment BA.

Q: 3. Prove that if P, Q, and R are three points on a line, then exactly one of the points is between…

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Q: Show that the following pair of a straigh line have the same set of angle bisectors  2x2+6xy+y2=0…

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Q: . For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line = (2,-1,-2) + t(3,1,-2)…

A: I have appended the formula used in the solution part of the question

Q: For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line r = (2,−1, −2) + t(3,1, −2)…

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

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Q: 9. If three distinct points P, Q, and R all lie on a line and if d(P, Q) = d(Q, R), then Q is called…

A: A line has no endpoints. A line is shown by two arrows on both ends. Whereas a line segment is part…

Q: al to the line given as :

A: Which of the following planes is normal to the line given as: x=2t+3, y=5t-7 , z=t-4

Q: Ex:O calkulate the gui for the distance formuld in a barred coordinate system defined by R = Ax,…

A: Given  that the matrix, A = 1-223 Let X = abcd So, that  X¯ = AX = 1-223·abcd               =…

Q: If three distinct points P, Q, and R all lie on a line and if d (P, Q)  = d(Q, R), then Q is called…

A: If three distinct points P, Q, and R all lie on a line and  d (P, Q)  = d(Q, R),

Q: 2. Sketch the set of points determined by the condition (a) Re(7 - i) = 2; (b) |27 + i| = 4.

A: Use the value of z to simplify the given equations. Now solve them to their simplest form and then…

Q: Which of the following conjectures is true for all cases about the lines in the image shown? A. If…

A: If two lines are cut by a transversal and,  if , Corresponding angles are congruent(i.e. equal),…

Q: This

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Q: Let et x= and y = . Find the distance betwen 2x and y

A: #  Given Data:     x=3,0,0     y=6,3,4

Q: 4. 3 2. 54 3-2 -1 1 2 4. -2 -3 -4 -5 -61 3.

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Q: olit he giren puints A and Bi and find he slype of the otr yht hoie clebermined by Hen d aper…

A: Given points are, A1,2B2,-1 The formula for finding the slope of the straight line is, m=y2-y1x2-x1

Q: Consider the line segments[1,2] ={x∈R|1≤x≤2} and [0,3] ={x∈R|0≤x≤3}. Show that[1,2]and[0,3]are…

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Q: 2 Statement 4 3 Qs = QS 5 QS bisects PR SP SR P Validate S ZOSP ZQSR QS bisects PR Prove: PORQ This…

A: QS⊥PRQS bisects PR

Q: Show that the vertices of any rectangle are co-circular by using the converse of the Power of point…

A: Geometry

Q: If ?1 is the line through ?(1,2,7) and ?(−2,3, −4) and ?2 is the line through ?(2, −1,4) and ?(5,7,…

A: Given that 1 is the line through (1, 2, 7) and (−2, 3, −4). So the direction ratio of line 1 is =…

Q: For trangle XYZ, points A, M, and P are the points of intersection of the altitudes, medians.…

A: In XYZ A is the point of intersection of altitudes. M is the point of intersection of medians. P is…

Q: Suppose n is an integer and z-z =r is a contour traversed once in counter clockwise, then dz = 2 Ti…

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

A: Answer: ∠1 ≅∠3  .

Q: If V is the midpoint of UW and TX, which of the statements is true? W

A: Given : V is midpoint of UW⏜ and TX⏜.

Q: / ife refresents the Segment of the line from Z-2 toZ-zi Kt frave Withouet finding the Kilke of the…

A: In both parts we can use the formula ∫Cf(z)dz≤ML where M is the upper bound of |f ( z )| over C and…

Q: Find the distance from (-5,9, –12) to each of the following: 1. The xy-plane. Answer:

A: Given point :-  (-5,9,-12) To find:- Distance of given point to plane xy

Q: If F =, and C is the line segment from (0, 0) to (1, 1). Then is equal to C O a.2e +2 -1 Ob. 2e 2e-2…

A: The given vector function is F→ = -e-x, -e-y. The line segment C is from (0,0) to (1,1).We have to…

Q: Family OF lines parring through (0, -4)

A: Given that family of lines passing through (0,-4). To find differential equation based on above…

Q: O -L -5) O4-

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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: Given: Line segment PQ has a length of 3(x+ PQ = QR, and QR = 84 %3D Prove: x = 21

A: Here we have to select the reason that best supports statement 6 in the given proof,

Q: Shaw that if Pu: R"> R^ is a onto a line and VER then; prejeetion

A: Given : Pu :ℝn→ℝn is a projection onto a line and v∈ℝn To show : ∥Puv∥≤∥v∥

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: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: P-4, 1 & Q3, -4

Q: Let a and b be positive numbers. Find the length of theshortest line segment that is cut off by the…

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Q: Which lines, if any, can be proved parallel given the f

A: Given that: Diagram :

Q: Which of the following denotes the length of a line segment with endpoints A and B?

A: Answer: B) AB¯

Q: 3- The tangont line to the cutve af the point (3,h)

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Q: 1. IN EACH CASE STATE WHETHER THE LINES ARE PARALLEL OR NOT GIVE REASONS FOR YOUR STATEMENT: 41 80 F…

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Q: By definition, two segment labeled QR and QS where Q is Between R and S must exist with which of the…

A: Let's find.

Q: Write down an explicit bijection between the following sets a. The interval (-2,1] and the unit…

A: Given:-             Write down an explicit bijection between the following setsa. The interval…

Q: What is the distance between the following points? 4- 17 -8-

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Q: ng actre za is a y points ere are allel line: em and

A: 1.a. Students who are good in Mathematics are smart.b. Josiah is good in mathematics then she is…

Q: If the points (h, 0), (a, b), and (0, k) lie on a line, show that 1 + k h

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Q: Suppose n is an integer and z-z=r is a contour traversed once in counter clockwise, then dz 2 Ti if…

A: Since it is the standard result which is true for n=-1 which proof is given in next step.

Q: 3.2. (a) Use the lines through the point (1, 1) to describe all the points on the circle 1 + y? = 2…

A: We can draw a line ML passing through the points P(1,1) and M(x ,y). Let the slope of L be m. We can…

Q: Q

A:

Q: Is the distance between a and b the same as the distancebetween b and a?

A: By Definition, The distance between two numbers is defined as distance = a - b  so, its an…

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.…