If A = ( - 1, 2) and B = (3, 4), find AB and redraw it (a) in standard position and(b) with its tail at the point C = (2, - 1).

Q: (6,6); parallel to 2x-5y=-7

A: Two lines are said to be parallel when they have the same slopes.Equation of a line in…

Q: find the angle between the 3x lines y 4 З and 5x - 2у %3D 10. -

A: The two lines are as follows y=3x4-3 and 5x-2y=102y=5x-10y=52x-10 comparing with y=mx+c where m is…

Q: The equation of a line of passage to the point (3,3) and is parallel to the line y=1/2x+2 is?

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

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Q: What equation is perpendicular to the line y = -2x + 3 through the point (0,2)?

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Q: Find the point on the line x/a + y/b =1  that is closest to the origin. Be sure to enter it as an…

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Q: How find the pistance from fant (1,3) and Line y -4

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Q: -) that passes through (-1,3) that is parallel to 2x – 5y = 1

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Q: Which of the following lines is perpendicular to the line   y  =  1/2x + 1   and contains the…

A: Consider the given line y=12x+1                                … 1

Q: Find |22z ds, where C is the line segment from (0,6,2) to (-3,12,7).

A: Given  ∫Cx2z ds, where C is the line segment from 0,6,2 to -3,12,7 To do  Find ∫Cx2z ds

Q: Find the distance between the point P(-2,4) and the line 3x-4y 12

A: Find the distance from the point P (–2, 4) to the line 3x – 4y = 12.

Q: Find an equation of the line passing through the point(1,6) that is parallel to the line y=5/9x+7

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Q: Find x²z ds, where C is the line segment from (0,-5,4) to (2,-7,8)

A: C is line segment from (0,-5,4) to (2,-7,8). parametric equations of C are: r(t)⇀=(1-t)r0⇀+tr1⇀  ,…

Q: What is an equation of the line that passes through the point (8, –7) and is parallel to the line x…

A: Solution:

Q: Find an equation of the line L.   L is perpendicular to y=3x through point (2,6)

A: Compare y=3x with y=mx+bSo, m=3Slope=3

Q: What is he symmetric equation of the line that passes through the points (3, 0, 11) and (2, 6, 7)?

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

A: The given equation of the line is, y=x+1 Let the point x,x+1 is closest to the point 4,1 Using…

Q: Find a point on x axis which is equidistant from A(2,-5) and B(-2,9)

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Q: Give the equation of the line passing through the point (– 3, – 9) that is parallel to y =

A: We will find the equation of the line.

Q: Find the point on the line 3x + y= 9 that Is closest to the point (-5, 1). (x, Y) - (

A: According to question given that Line 3x+y=9, closest to the point (-5,1)We have to calculate the…

Q: The distance from the point (2,1) to the line  4x-3y+5=0 is

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Q: Find an equation of the line passing through the point (2,1) that is perpendicular to the line…

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Q: The line perpendicular to y=-x+1, passing through the point (–4, 2)

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Q: Find the distance from the point (-6,-2,0) to the line a(t) = ( – 1, – 2, – 5)t + (3, – 6, 6)

A: We  use the definitions

Q: | xyz2 ds, C is the line segment from (-1, 5, 0) to (1, 6, 5)

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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: The line passes through the point (4,4) and is parallel to the line 3x-y=6

A: Given, equation of line and point

Q: The line passes through the point (-1, 4, -5) and is parallel to v = 2i – j. %3D

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Q: Find the distance between the points (1,1) and (3,9) along the line y=4x-3

A: Since the points (1,1) and (3,9) lie on the line, so the distance between the points along the line…

Q: Find the equation of the line that passes through point (1,3) and is rpendicular to the that passes…

A: Calculate the slope m for line passing through (-3, 8) and (5, -7).…

Q: Determine Duf(-1,3, 2) for f (x, y, z) = e2ay° + 4x²yz in the direction (3, -2, 5). V =

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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: Find the point on the line y = 2x + 3 that is closest to theorigin.

A: Given equation of line,  y = 2x + 3 To find the point on line that is closest to the origin.

Q: that

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Q: What is the coordinates of the point on the line y = 2x +1 which is closest to the point (2, 1)?

A: The point on the line y=2x+1 which is closest to point (2, 1) is the point through which a line…

Q: Find the distance between the points (2, −1, 3) and (1, 0, −2).

A: To find the distance between the points (2, −1, 3) and (1, 0, −2).

Q: Find the values of δƒ/δx and δƒ/δy at the point (4, -5) ifƒ(x, y) = x2 + 3xy + y - 1.

A: ddxxn=n xn-1

Q: Find the line L passes through the point (-2,2) and perpendicular to the line L`: 2x +y = 4.

A: Given, The line L passes through the point -2, 2 and perpendicular to the line 2x+y = 4    We have…

Q: Find 1x²z ds, where C is the line segment C from (0,-3,-5) to (2,1,-5)

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Q: (-2,4) parallel to y=-3/2x+3

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Q: So Find x²z ds, where C' is the line segment from C (0,-5,4) to (-6,-4,3)

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Q: Find an equation of line L. (1, 3) х (-3, –1),

A: We find the slope of the blue line first For that, we find the slope between (-3,-1) and (1,3) So…

Q: Find the point on the line 2x + y = 9 that is closest to the point (-4, 3). (x, y) =

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Q: 9. Solve for x and y that make the lines parallel.

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Q: Find the foot of the perpendicular drawn from (4,1) upon the straight line 3x – 4y + 12 = 0 -

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Q: Find x²z ds, where C is the line segment from (0,6,4) to (1,3,-2) C

A: ∫C y ds,  C: x=t2, y=t,  -2≤t≤3   dxdt = 2t,   dydt= 1∫Cy ds = ∫-23 t  (2t)2+1 dt=∫-23 t  4t2+1…

Q: Suppose that the elevation on a hill is given by flx, y) = 200 – 4,² – 5. From the site at (4, 2),…

A: Given query is to find the direction of the rain's run off.

Q: At point (1,y), what is y?

A: Note:- If two points is given in Cartesian form like  (2,5)  Then  x=2 and y=5 Means first one is…

Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0.

A: Introduction :

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.