Write a paragraph proof of the following. 1. Point X is the midpoint of WY and Point Y is the midpoint of segment XZ Prove that WX = YZ 2. Point H is the midpoint of JN, prove that JH = HN.

Q: Use the Theorem of Pythagoras to find the length of the line segment y = 3xfrom (1,3) to (2,6), and…

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Q: P = (9,6,1) R = (9,8,5) Find the point such that R is the midpoint of PQ.

A: given R is midpoint of PQ  if two points is (x1,y1,z1) and (x2,y2,z2)then coordinates of midpoint is…

Q: Let p(-1, y, 2) and Q(2, 0, 4) if the length of PQ is SQRT2 find y

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Q: a circle is 24 cm and the distance is

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Q: XM bisects angle YXZ and angle YMZ  prove XM bisects angle YKZ

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Q: 4. Evaluate S. (z - 4) dz, where r is a contour from the two line segments, the first from z = -3 to…

A: The given question is related with complex integration. We have to evaluate the integral,…

Q: FADEFIS an isosceles triangle with base DF, what is the value of x?

A: Given triangle DEF is an isosceles triangle with the base DF.Soa)DE = EF5x - 3 = 3x + 75x - 3x =…

Q: -7) 2) (3,-2) EXERCISE-2 (LOCUS) LEVEL-I us of the point, the sum of whose distances from the…

A: The Locus of the point, the sum of whose distances from the coordinate axes is 9 is Explanation:…

Q: let γ be the line segment joining 0 to 1+i. then the value of ∫γzdz is

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Q: Find the angle between v and w if v · w = 1/2 ||v|| ||w||.

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Q: Use the applet to translate quadrilateral ABCD 2 units left to create quadrilateral A'B'C'D', then…

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Q: 4. Evaluate S. (z – 4) dz, where r is a contour from the two line segments, the first from z = -3 to…

A: Contour integrals or line integrals along a path C   can be written as ∫Cf(z) dz=∫abf(z(t) z'(t) dt…

Q: 2. Let c be the line from 5 to 2 + 3i. Find i. S. zdz ii. S. ždz

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Q: Find the shortest distance from the point (1, 1, 4) to the cone z = You may round to the nearest…

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Q: Evaluate . F dr where F(x, y, z) = zi + x²j + yk and C is the line segment from (1,2,3) to (4,3,2).…

A: Given Fx,y,z=zi^+x2j^+yk^. We have to evaluate ∫CF⋅dr, where C is the line segment from 1,2,3 to…

Q: All 3 parts.

A: To find the slope of the tangent, we need f'(64)

Q: 3. The distance between two distinct points (x1, y1) and (x2, y2) is given by the formula

A: Given: Points x1, y1 and x2, y2

Q: 15. M is the midpoint of line segment PQ, and R is the midpoint of TS. If PM = MQ = a and TR = RS =…

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Q: Find the distance d from the point P = (6, 1, 4) to the line r(t) = (4 + t)i + (1 + 2t)j + (1 +…

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Q: 1.5 If A = 5a, + 3a, + 2m, B-a, + 4a, + 6a, C = 8a, + 2a, find the values of a and 3 such that aA +…

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Q: Let P(6, – 2, 2) and Q(0, 0, 0) be two points in R³. Find the distance between P and Q. - PQ

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Q: Ex+2, Find x, OE , and PR

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Q: 3. The endpoints of QR midpoint M. are Q(1,6) and R(-7,3). Find the coordinates of the

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Q: The midpoint of AB is at (-5, 3). If A = (4, -6), find В. B is:(

A: Mid point: If Ax1, y1 and Bx2, y2 are any two points then, the coordinates of the midpoint of AB are…

Q: In kite ABCD below, point E is the midpoint of BD. What are the coordinates of point D? E(10,4) В…

A: Mid point of the line joining two points (x1,y1)  and (x2,y2) is given by M=((x1+x2)/2 , (y1+y2)/2)

Q: If å = 4i + 2j + 4k ,b = -2i + 4j – 3k and ĉ = 4i + 5j. If å + xb is perpendicular to ĉ then find x.

A: Solution:-

Q: 3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The corners…

A: a)Co-ordinates of GG0+7.52,0+02,0+02=G154,0,0Co-ordinates of P∵P lies on the  xy planeso…

Q: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

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Q: 36) Given the points P(3,2) and Q(6,6) a. Find PQ b. Find the midpoint of PQ

A: solution:- use formulaes from coordinate geomatry

Q: LET AB BE A 17 FEET LADDER, WHICH LEANS AGAINST A WALL. THE LADDER MAKES A 60 DEGREE ANGLE WITH THE…

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