Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1,√5). Find the coordinates of the point S on line segment PR such that line segment QS is perpendicular to line segment PR.

Q: Find the distance between the point (5, 1) and the line y = 3x + 1. O 3V10 O 7/10 O 9/10 O 5V10

A:

Q: Plot the points A = ( - 1, 8) and M = (2, 3) in the xy-plane. If M is the midpoint of a line segment…

A: We have the following information    We have to plot the points A = ( - 1, 8) and M = (2, 3) in…

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

A:

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

A:

Q: Find r so that the line through (2,6) and (-4,r) a).parallel to 2x-3y=4 b). Pendicular to x+2y=1

A:

Q: Use the above formula to find the distance from the point to the given line. (5, 3, -3); x = 1 + t,…

A:

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 distance between the point (-3, 1, 5) and the line given by x = 5+t, y = 1- 2t, and z = 3-…

A: Given : Point A ( -3,1,5) x = 5+t  y=1-2t  z=3-t

Q: Find the coordinates of the midpoint of the line segment PQ. P(x-Z, r), Q(x + z, r) Select one: O A.…

A: The mid-point formula of a line segment is, x,y=x1+x22,y1+y22 where x,y is mid-point of the line…

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

A:

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

A:

Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

A:

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

A:

Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Find the distance of the point (2, 2, –5) from the line r(t) = (1+4t, –1+ 4t,7 – 3t) %3D swer:

A:

Q: Find the point P on AB that is one-third of the distance from A(-1, 2) to B(8, 5). y 10 8. P -10-8…

A: Given points A(-1, 2) and B(8, 5). To find point P which divides the line segment in the ratio 1:3.…

Q: Find the distance between the point (−3, 5, 1) and the line given by x = 1 + t, y = 5 − 2t, and z =…

A:

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

A:

Q: Find the coordinates of the missing endpoint given that P(6, 3) is the midpoint of NQ and N(5, 4)?

A: Coordinates of mid point Mx,yof the line joining two points Ax1,y1 & Bx2,y2 are given…

Q: Find the distance from point P to line L.  P(3,-1,4), L: (x-4)/-1 = (y-3)/2 = (x+5)/3

A:

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

A:

Q: Find the value of  x for which the distance between the point P(2, -3) and Q (x, 5) is 10

A:

Q: Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that…

A: y=2x-4 and y=-4x+20 We need to find the area of the triangle that lies in the first quadrant (with…

Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: Find the shortest distance between the point Q(2, 0, 0) and the line segment joining the points…

A: Formula used: Distance between the point and a line is, D=PQ×uu Where u=P2-P1

Q: The points P, Q and R have coordinates (8, 7), (−2,−1) and (−6, 5) respectively. Show that the…

A: The point P is (8,7) and find the equation of the line passing through the point (8,7).The line…

Q: d the eqation of the line that passes through A(1,2,1) and intersects the line x+1 у-2 z+1 %3D at…

A: Topic:- geometry

Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Find the point ( x, y) such that (1, 3) is the midpoint of the line segment connecting а. (х, у) and…

A: NOTE-Since you have posted a question with multiple sub-parts, we will solve first three subparts…

Q: Determine the midpoint M of the line segment with endpoints U (2,7) and V(12, 8).

A:

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: Find the distance between the points: (3, 7) and (2, 12) ww.. A

A:

Q: Find the value of z that makes lines u and v parallel. 85° 12x+ 1

A:

Q: C. Show that the lines with symmetric equations (x y z) and (x+1 are skew, and find the distance…

A: L1 ;  x=y=z     x-01 =y-01=z-01  x1=0    y1=0     z1=0α1=1    β1=1      γ1=1L2:  x+1=y2=z3…

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: The lines joining the origin to the point of intersection of the line lx+my=1 and y²=4ax are at…

A:

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

A:

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: Which of the following mathematical models is used to determine the distance between two points…

A:

Q: on the line ye -2x +8 that 1-) Find the point IS Close't to the onigin.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: find the distance from the point to the line (2, 2, 0); x = -t, y = t, z = -1 + t

A: Given information: The point to the line is (2, 2, 0) and x = -t, y = t, z = -1 + t. Calculation:…

Q: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

A:

Q: Find the midpoint M of the line segment joining the points P = (-7,-6) and Q = (-1, 2). M = OD %3D

A: We have to find the mid point between the two given points  P(-7,-6) ,Q(-1,2) .

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

A:

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l.

A: In a 3 dimensional space, a point and a line can be at infinite number of distance from each other,…

Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3- 2t ,y=-2t+1,z=t is

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

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.