Q.2) The horizontal line h in space placed in position that the coordinates of its two ends are D(5,5,2) and E(?,?,?). If the point E is located on the straight line m[A(1,3,1),B(6,2,3)], draw the two projections of of the horizontal line h.

Q: Let l,,l2,lz be the lines X(t) = (1,1, 2) + t(1,2,3), X(s)= (9,8,11) + s(2,1,1) and X (r) = (0,0,0)…

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Q: 3) Let M be the midpoint of a line segment joining two points A(20, -1) and B (4, –9). Calculate the…

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

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Q: 1. Show that the lines having the equations 4x- 3y + 12 = 0 and 8x 6y + 15 = 0 are parallel.

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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: 2. Suppose A, B,C, D e E³ are distinct points occurring in that order ong a straight line. a) Show…

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Q: Show that the quadrilateral with the given vertices is a parallelogram. E(-5,-2), F(-3,3), G(3,5),…

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Q: 5. Find the bisectors of the angles between the lines, 2x-y 1 and 11x +2y= 5.

A: Given, lines, 2x-y=1,  11x+2y=5 now find angle bisectors between lines we know the formula of…

Q: Find the equation of the plane through P(4, 3, 6) and perpendicular to the line joining P(4, 3, 6)…

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Q: The line in R that is parallel to the y-axis and passes through the point (1, 2, 3) has equation + t…

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Q: 2. Evaluate . 3x – 6y ds for C is the line segment from (6,0) to (6,6).

A: Let C be a piecewise smooth curve defined by, Let P and Q be two continuous functions of x and y…

Q: If M(4, 3) is the midpoint of the line segment AB, and if A has coordinates (1, -1), find the…

A: M4, 3 is the midpoint of the line segment AB and the coordinates of A are 1, -1.

Q: B. Find the distance between the point (1. 1.3) and the line =z-3) OMI NOTL

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Q: Given the points F(8,4) and G(-7,-6) what are the coordinates of the point that partitions the…

A: Given that points are F8,4 and G−7,−6. We have to find the coordinates of the point that partitions…

Q: 15. Find the angle between the straight lines I, and l, which are defined by x-2 y+1 =1-z. 4:x=1+2t,…

A: The angle is, 85.75°  The detailed solution is as follows below:

Q: 9. Determine the point of intersection of the following two lines: L₁: (x, y, z) = (1, 2, 1) + t(3,…

A: Find value of parametric by equating L1  and L2.

Q: Let C be the line segment connecting the points P(−2,1,−4) and Q(5,−4,3). Evaluate ∫C(2x+4z)dy…

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Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: Consider the line which passes through the point P(5, -5, 5), and which is parallel to the line x =…

A: The direction vector of the line  given by:        x=1+4ty=2+1tz=3+3t is :    r→=123+t413 So, The…

Q: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

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Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: 10. If M is the midpoint of the line AB where A has coordinates (- 6,5) and B has coordinates (4,3).…

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Q: Let M be the midpoint of a line segment joining two points P(8, -2) and Q (6, 10). Calculate the…

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Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1,√5). Find the coordinates of the point S on…

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Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: The midpoint of a segment can be found using the formulas for a directed line segment, x = (X2-X1) +…

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Q: Use the result in Exercise 21 to find the equation of the line that contains (5, – 1) and is…

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Q: 9. In the standard (x, y) coordinate plane, line e contains the points (3, 5) and (5,8) and line m…

A: We have to find out k

Q: Consider the following pair of points. (9,−9) and (−5,9) Step 2 of 2: Determine the midpoint of…

A: Consider the provided points, 9,-9  and  -5,9 Determine the midpoint of the line segment joining the…

Q: 4. In the xy-plane, the line.determined by the points (3, a) and (a, 12) passes through the origin.…

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Q: Find the Cartesian equation of the locus of points satisfying PA + PB = 12, where A is the point…

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Q: 7. Reflect parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,–4) in the line y = -x.…

A: Reflection in Y axis  : (x , y ) → (-x , - y )

Q: Find (i) the undirected distance between point A and b, and (ii) the midpoint of the line segment…

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Q: Find x'z ds, where C is the line segment from (0,2,-3) to (6,0,-6) C

A: To find:∫Cx2z dsThe line segment is from 0, 2, -3 to 6, 0, -6

Q: 1. Determine the intersection (if any) of the lines I1: (x, y, z) = (2,0, 9) + s(1, 2, 3), s e R,…

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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: 10. In the standard (x, y) coordinate plane, line r contains the points (6, 5) and (b,-5), and line…

A: Given problem is :

Q: Use the result in Exercise 21 to find the equation of the line that contains (4, 5) and is…

A: Given- 2x+3y=6 To find- The equation of the line which is passing through the point 4,5 and…

Q: Find the distance between the given point Q and the given line. Q(- 9, 1, 10); x= - 5+ 3t, y = 1-t,…

A: Given that, the point is Q-9,1,10 and x=-5+3t, y=1-t and z=7+4t. Obtain the value of rt=xi+yj+zk.…

Q: Consider the points a, b, c, d and the lines L, M in the following figure.

A: Given a graph containing the points a, b, c, d and lines L, M

Q: 7. Given that M4,6) is the mid-point of the line segment joining C(2, -3) and D, find the…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Prove that if P(I, y) be any point on the line segment joining R(11, Y1) and P2(12, Y2) then I= I1+…

A: Let P divides P1 and P2 in the ratio k : (1-k) x=kx2+1-kx1k+1-kx=kx2+x1-kx1x=x1+kx2-x1 Similarly…

Q: Given the points M(-6,-4) and T(9,16) find the y-coordinate of the point Q on the directed line…

A: We have to solve

Q: Find the midpoint M of the line segment joining the points A = (7, 1) and B= =(1, 5). %3D %3D M = OD

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Q: Determine all points P(x,y) such that PA = PB. A = (2,3) and B is on the line y=-3

A: solution:- A(2,3) B(0,-3)

Q: Find the x- and y-coordinates of the labeled point. Ay 10- The coordinates of A are 8- (Type an…

A: The labeled point lies on the x- axis . So its y-coordinates is zero .

Q: If M(6,8) is the midpoint of the line segment AB and if A has coordinates (2,3), fınd the…

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Q: Use the result in Exercise 20 to find the equation of the line that contains (4, 5) and is parallel…

A: We know the important theorem is that the graph of Ax+By=C is parallel to the graph of Ax+By=D.…

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.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.