Based on the figure below, if the line equation is given by 2, y, z| 1,0,2| +t[1,3,0| and the point S is located at (2, 1,2), the coordinates of the point Pare S. Line

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

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Q: Consider the line which passes through the point P(-3, –3, –1), and which is parallel to the line x…

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Q: 8. Find the point (x. y) such that (1, 3) is the midpoint of the line segment connecting a. (x, y)…

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Q: In Cartesian space, the point form of a line is e: (x, y, z) = (2 + r, -3 + 2r, 5 – 5r). - 3. a)…

A: Given: The point form of a line is l:x,y,z=2+r,-3+2r,5-5r. Calculation: (a) It is observed from the…

Q: The distance between the points (-3,-5) and (2, 7) on the coordinate plane is given as y+. What is…

A: Distance Between Two Points We use the Pythagoras Theorem to derive a formula for finding the…

Q: Find all points with coordinates of the form (a, a) that are a distance 3 from P(-2, 1).

A: Given: P(-2,1) and distance is 3. To find the other coordinate point.

Q: The line perpendicular to y=x+5, passing through the point (3, 2).

A: You know that if you multiply slopes of two perpendicular lines you will get -1. m1 x m2 = -1

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

A: Equation of the line :       x-x0a = y-y0b = z-z0c=k ; where x0,y0,z0 is a point and a,b,c is the…

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: Consider the line with equation OP + td where P = (1,1,0) and d = (-1,2, 1). Notice that P is on the…

A: Given that the equation of the line is OP+td where P=(1,1,0),d=(-1,2,1) And given that Q=(1,2,-1)…

Q: EXERCISES 4:Find the tangent line at the given point xy = -4, (2,-2) 1. x² - xy + y? = 7, (-1,2) 2.

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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: #3 Find the line equation(s) of the line(s) through point P(1, 0, 1) that meets the following line…

A: Given :  Given:P(1,0,1)L: x,y,x=1,2,0+t2,-1,2P0=1,2,0Aim: To find a line(s) through point P,…

Q: Find the point(s) on x = 3 - y that are closest to point A = (1,0).

A: Given: Curve x=3-y2 and a point A(1,0).

Q: Find an equation for the set of points P(x, y) in a plane the sum of whose distances from two fixed…

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Q: Based on the figure below, if the line equation is given by 2, y, z= [3,0, 6+ t(1, 2,0] and the…

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Q: Let l be the line (1, –1,1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. %3D…

A: Given the line equation l is 1,-1,1+t0,2,1 and the point is Q=1,0,1. Find the distance from Q to l.

Q: Let A be the point with coordinates (-3, 2, -1) and let B be the point with coordinates (2, 0, 0).…

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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. %3D

A: Given line is                                                       l:1, -1, 1+t0, 2, 1 vector…

Q: Consider the two points (4, –3) and (5, 7). The distance between them is: The x co-ordinate of the…

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Q: In Cartesian space, the point form of a line is e: (x, y, 2) = (2 + r, -3 + 2r, 5 5r). a) Find the…

A: In cartesian space, the point form of a line is  l : (x, y, z) = (2+r, -3+2r, 5-5r).   a) Find the…

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

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Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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Q: 3- The line jaining the origin and Point_of intersection of the linesr(X=l+2t_ ys-3+4Ł,2=t) aul (x-…

A: Given that: Lines are: L1: (x=1+2t, y=-3+4t, z=t) and L2: (x=-2+3t, y=-5+3t, z=-12+34t)

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: 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: 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: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Find the relationship between x and y such that point (x,y) is equidistant from the points (7,1) and…

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Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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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: 7. Find the distance from the point A to the line through the points B and C where A, B, and C have…

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Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

A: We will solve the problem

Q: Find the value(s) of x such that the distance between the points is 5. (2, -1), (x, 2)

A: Distance between the points 2,1, x,2 is 5. use distance formula:    Distance between the points…

Q: Consider the line which passes through the point P(-2, 4, 3), and which is parallel to the line x =…

A: Consider a line  L1:x=1+7t,y=2+7t,z=3+4t Point : −2,4,3

Q: Points F, G, and H are collinear such as FG: FH = 1/3. If directed line segment begans at F(-5,-1)…

A: Given that F,G,H are collinear FG:FH=13 also F(-5,-1) and H(4,-1) find G

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: Find the point(s) on x = 3 – y? that are closest to point A=(1,0).

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Q: 1. Which of the following points in the standard (x, y) coordinate plane is farthest from the…

A: Find the distance of each given point from origin Using distance formula.

Q: 4. Find the line(s) containing the point (–1,4) and lying at a distance of 5 from the point (6,3).

A: (Note: We are entitled to solve only one question at a time) To Find: The lines containing the point…

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

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Q: 9. Reflect the point (3, 2) over the following axes or lines. Reflection Over New Coordinates х —…

A: 3, 2. Reflection over x-axis: When a point x, y is reflected over x-axis, then the new coordinates…

Q: Consider the two points (4,2) and (10,4). The distance between them is:   The x co-ordinate of the…

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Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

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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: Find the length of the tangent to a circle from point of tangency to point (8,2) . The circle is…

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Q: 2. Let l be the line with equation x = 2y = z +3 and let P be the point (1, 1, 1). Consider a line…

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