If the point (4, 1) is the midpoint of the line PD , where P (x, 3),  D (7, y)   ,  find the value of x, y

Q: Is there a value for k that would make the line between the points (k,2) and (3,8) horizontal? If so…

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Q: A line passing through (0, –3) and is perpendicular to y =;x – 4. х —

A: The given line passing through the point 0,-3 and it perpendicular to the line y=52x-4. Calculation:…

Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: Find an equation of the line that satisfies the given conditions. Through  (1, −1);   parallel to…

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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 an equation of the line that satisfies the given conditions. Throught (2,6); perpendicular to…

A: y=1;(2,6)

Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

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Q: Find the point of intersection of the lines with the given equations. 6x + 4y = −10   and   6x + 9y…

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Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: The temperature of a rectangular plate bounded by the lines x = ±1, y = ±1, is given by T = 2x2 −…

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Q: Is there a value for k that would make the line between the points (k,2) and (3,8) vertical? If so,…

A: Given points K,2 and 3,8If the given line is vertical then the line is parallel to the y-axis…

Q: Find the point (xo, yo) on the line 4x + 9y = 12 that is closest to theong1n.

A: Given: 4x+9y=12 Let the distance between the point (x0, y0) and origin be D As it is given that the…

Q: In the equation of the line                      ⟨x, y, z⟩ = ⟨x0, y0, z0⟩ + t⟨x1 - x0, y1 - y0, z1 -…

A: The given equation for the line is,

Q: Evaluate ∫C x ds, where C is the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).

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Q: The slope of the line tangent to the graph of 3x +5In y 12 at (2, 1) is 12 (A) 12 (B) 5. (C) 12 4.

A: Given that 3x2+5lny=12To find : Slope of the tangent line at point 2,1Solution :

Q: Q)Suppose that one line is parallel y=13x+ 13 and passes through (15,7). Where does that line cross…

A: Given :  y=13x+ 13  compare with y = mx + c slope m = 13

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

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Q: find value(s) of k so that the lines described by 3x = 2y+11 and kx = 40 - 6y are perpendicular

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Q: If a line intersects the x-axis at 'r' and the y-axis at '1/r', at what point (x,y) does it…

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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: What is an equation of the line that passes through the point (–6, –6) and is paralle to the line x…

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Q: ons 5y−5x=305y−5x=30 and y=−x+3y=

A: we have to tell whether the lines represented by the equations are intersecting , parallel, or…

Q: If the line joining the two points (5,4)(5,4) and (3,−k)(3,−k) is parallel to the line kx−9y+11=0…

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Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r,…

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Q: Find the equation of a line perpendicular to y=−x−1 that contains the point (1,2).

A: We have to find the equation

Q: If Y (-7,-4) and Z (5, 2), find the slope of a line perpendicular to YZ O 2

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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: If C is the line segment connecting the point (x1, Yı) to the point (x2, Y2), find the following. x…

A: “Since you have asked multiple questions, we will solve the first question for you i.e. (a). If you…

Q: Show that the equation of the line in R² can be written as х det 1 X1 У1 X2 У2.

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Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: We are given two lines L1 and L2 in 3d, and we have to find the closest points x1 , x2 such that the…

Q: The coordinates of a point on the line x+ y+1 = 0 which is at a distance /2 units from the line 3x +…

A: Given: The line x+y+1=0 which is at a distance 2 units from the line 3x+4y-2=0 To find: Coordinates…

Q: Find the value of x for which line a is parallel to line b.

A: It is given that,  line a and b are parallel lines,

Q: Show that the line with intercepts (a, 0) and (0, b) has the following equation. x/a + y/b = 1, a ≠…

A: The two points are given as , a,0 and 0,b. To find the line with intercepts on given points.…

Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.

Q: What can you conclude if you know that the point (p, q) lies on the line y = mx + b?

A: We have to conclude if the point p, q lies on the line y=mx+b. We know that if any point is lying on…

Q: Let A(x,y) be the point on the line y = x + 1 that is closest to the point B(2,0). Then the square…

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Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

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Q: Find the distance between lines x + 3y = 5 and x + 3y = 25.

A: The distance between two parallel lines can be calculated using the formula,

Q: Given that the line kx − y = 4 is perpendicular to the line kx + 9y = 11, find the value of k

A: Given query is to find the value of k.

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

A: We need to find the distance of the point (1,1,5) and the given line.

Q: Evaluate (x + y) ds, where Cl is the line segment from (-2, 1, –5) to (-1, –1, –2).|

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Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. *

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Q: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

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Q: Determine the value of A so that the line whose equation is Ax+y−7=0 is perpendicular to the line…

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Q: Is it true or false that the equation the distance from the point A(1,2, 6) to the line x + y + 2z =…

A: The line is l:l:x+y+2z=62x-y+z=9 and the point is 1,2,6

Q: Find an equation of the line satisfying the following conditions. Through point (1, –5);…

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Q: Write an equation for the line through the point (1,3) parallel to the line y = x + 10. Oy=z O y =…

A: Given query is to find the Indicated line.