In Exercises 29 and 30, find the distance from the point to the line. 29. (2, 2, 0); x =-t, y = t, z =-1 + t 30. (0, 4, 1); x = 2 + t, y = 2 + t, z = t

Q: (1) What is the relationship etween lines 11 and 12? where L:x = 2, y = 1+ 2t, z = 1+t L2:x = 4 -t,…

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Q: Find the distance, to the nearest hundredth, between the given points. P1(0, 7) and P2(-4, 8) Find…

A: We need to find the distance.

Q: Find the egmation for the Line" dhint passes through the point (,0) and parallel to the Line…

A: NOTE:Kindly repost the other question as a separate question.

Q: Find the point on the line 5x + y = 5 that is closest to the point  (−4, 1).   x,y= (  , )

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Q: Which point(s) lie on the line (x, y, z) = (2, –1, 5) + n(1, 2, - 1)? a) (1,- 3, 4) %3D b) (5, 5, 2)

A: The given line is  (x,y,z)=(2,-1,5)+n(1,2,-1) compare  with general equation of line in a space

Q: Sketch the translation of the triangle with the rule (x, y) → (x+5, y+1). T 5 -10 -5 5 10 --5

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Q: 4. What is the equation of a line parallel to the diameter of circle A, with a center at (-5,7) and…

A: Given query is to find the line which parallel to the given line.

Q: Find the distance of the point (3, 2, –4) from the line r(t) = (1+ 3t, –1+ 2t, 3 – 3t).

A: for finding distance of the point3,2,-4 from line rt=1+3t, -1+2t, 3-3t we assume a point1+3t, -1+2t,…

Q: Find the intersection point of the two lines: [x, y, z] = [–2, 3, –3] + t[1, –1, 2] and [x, y, z]…

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Q: What is the distance between points (5, 2) and (1, -3) on a coordinate plane? 4.1 © 8.5 6.4

A: We can use distance formula to find distance between two points (x1,y1) and (x2,y2).

Q: Find the point of intersection of the lines: y = 4x + 1 and y = -2x +4 %3D o (2,9) 으(4,2) ㅇ (4,3) O…

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Q: Find the EXACT distance (do NOT round) between these two lines. L1: [x, y, z] = [1, 3, 7] + t[–1,…

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Q: In Exercises 33–34, find the distance from the point to the line. 33. (2, 1, 3); x = 2 + 2t, y = 1 +…

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question…

Q: Sketch the translation of the triangle with the rule (x, y) → (x+5, y+1). T 5- -10 -5 10 -5- 5

A: The coordinates of vertices of the blue triangle (1st quadrant) are A1, 1, B3, 1 and C3, 5. Now, Use…

Q: Used to determine the distance between two points (*11) and (*, V2) d= V(*-*)2 +(2 -1)2 and (X2 d%3D…

A: Given that distance between points                                                 (x1, y1)  &…

Q: Find the distance between two lines ()1=4-x , y;=- (x+2).

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the distance from the point (3,-1, 4) to the line a = 4 – t, y = 3 + 2t, z = -5+ 3t.

A: Given: point 3,-1,4 and equation of line x=4-t, y=3+2t, z=-5+3t Formula: The distance between point…

Q: Let A be the point with coordinates (-3, -2, 3) and let B be the point with coordinates (2, 0, 0).…

A: To find the distance from point D to line l.

Q: Find the distance from the point (1, 2, 3) to the line x=0,y=2+5t,z=3+5t

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Q: if (u, v) and (s, t) are two distinct points in the plane, what is the distance between them?…

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Q: Find the distance from the point to the line.   (−4,4,−1)​; x=-3+3t, y=-1+t, z=1+2t   The distance…

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Q: find the distance from A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

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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: B) Find Duf of f(x,y.z) x + y? + 2? - 3 at point(1,1,1)in the direction of point (3,5,-3).

A: Take gradient at given point and take dot product with unit vector for directional derivative

Q: 3. Line ZW is parallel to line XY and line CD intersects both lines. 154° -Y X 3 4. Based on the…

A: Given To Evaluate m∠1 and m∠2?

Q: Find the distance from the point to the plane (2,-3,4) , x+2 y - 2 z = 13

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Q: In Exercises 33–34, find the distance from the point to the line. 33. (3, -1, 4); x = 4 - t, y = 3 +…

A: Note:We’ll answer the 33th question since we answer only one question at a time. Please submit a new…

Q: Find the distance of the point (4, 2, -4) from the line r(t) = (1+2t, 1+ 2t, 7 - 3t).

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Q: 2. In the standard (x, y) coordinate plane, a line segment with the endpoints (-1,3) and (4, 3) is…

A: Given: line segment with (-1,3) (4,3) is one side of the square . find the Area of the square

Q: Evaluate ryz ds, where C is the line segment from (3, 0, 1) to (0, 2, 5).

A: Given function is ∫Cxyz ds Given points are r1=3,0,1 and r2=0,2,5 We can write the given points in…

Q: Explain why the lines below are parallel. l: (x, y, z) = (2, 3, 4) + n(1, 2, - 3) and (2: (x, y, z)…

A: l1 : x, y, z=2, 3, 4+n1, 2, -3l2 : x, y, z=3, 7, -2+r-1, -2, 3 Here, The direction ratios of l1 are…

Q: What are the coordinates of the midpoint of segment GH with endpoints G(-2, 5) and H(4, 1)?  a (-6,…

A: midpoint of segment GH with endpoints G(-2, 5) and H(4, 1)

Q: Find a best straight line y = cx+d that best fits three points (1, 1), (–-1,2), (-2, 1). %3D

A: We have the equation of given straight line as y=cx+d            ⋯⋯1 If the points 1,1,-1,2 and -2,1…

Q: In Exercises 33–34, find the distance from the point to the line. 33. (0, 0, 12); x = 4t, y =-2t, z…

A: We’ll answer the 33th question since we answer only one question at a time. Please submit a new…

Q: Calculate the distance between the points K=(-3, -2) and c=(1, 1) in the coordinate plane. Give an…

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Q: Find general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

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Q: Find the distance between points P1(0, 0, 0) and P2(-6,-2,5).

A: Distance = x2-x1+Y2-Y1+z2-z1

Q: Determine the exact distance between lines l1: 7 = (5,–3,7) + s(3,-2, 5) and l2: 7 = (2,-7,9) +…

A: Here both the lines are parallel.

Q: Find the length of the line segment described by, (x,y,z)=(1,2,1) +t(-1,5,4)), where 0<t<5.

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Q: Using the rule (x, y)-(-y, x) find the image points: A(2, 3) B(-5, 6) C(-1,-3) B'(, ) C(, ) A'(, )

A: 30. Using the rule (x,y)→(-y,x) Find the image pointsA(2,3)       B(-5,6)…

Q: In Exercises 33-38, find the distance from the point to the line. 33. (0, 0, 12); x = 4t, y = -2t, z…

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Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: The midpoint of the line segment between P1 (x,y) and P2 (-2,4) is Pm (2,-1). Find the coordinates…

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Q: 5- Find the distance from the point to the line. a. (0,0, 12); x = 4t, y = -2t, z = 2t b. (0, 0, 0);…

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Q: Explain why the lines below intersect. l1: (x, y, z) = (2, 3, 4) + n(1, 2, – 3) and l2: (x, y, z) =…

A: Given : Vector equation of the line l1 : x, y, z=2, 3, 4+n1, 2, -3 Vector equation of the line l2 :…

Q: Let A be the point with coordinates (-3, -2, 3) and let B be the point with coordinates (2, 0, 0).…

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Q: 7. In the standard (x, y) coordinate plane, the point (2,7) is the midpoint of the line segment with…

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Q: Find the distance between points A(1,1,0) and B(1,0,1)?

A: A1, 1, 0 &amp; B1, 0, 1.

Q: 11b) Are the two lines perpendicular? Show work y (+5,6) 4 (1, 3) (-5, 0) 4 (-1,-2) 6.

A: Given,

Q: Find the value(s) of y such that the distance between the points is 6. (-6, 0), (-9, y)

A: Solve for the value of y

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.