Consider the points P = (3, 2, 1) and Q = (1, 2, 3) in R3. (a) What is the distance between P and Q? (b) What is the equation of the line that passes through P and Q? (c) What does the set of points in R3 that are equidistant from P and Q look like? Write a formula that describes this set of points.

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

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Q: The line segment that connects the points (-2,2) and (6,-1) Q intersects both the x and y axes.…

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Q: Find the distance between the points P = ( - 1, 3) and Q = (4, -2). Find the midpoint of the line…

A: (-1,3),(4,-2)

Q: Find the distance from the point to the line. (-4, – 2,1); x= 5 – t, y = 1- 2t, z = - 6 + 3t

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Q: Find an equation of the set of all points equidistant from the points A(-1, 5, 4) and B(6, 2, –1).

A: Given : A(-1,5,4) and B(6,2,-1) Let P(x,y,x) be at equidistance from A  and B Now find the distance…

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 the distance between the given pair of points: -5 and 17

A: Solve for the distance between the points

Q: Write the distance d between the point (3, 1) and the line y = mx + 4 in terms of m. Use a graphing…

A: We have given a point (3,1) and an equation of line y=mx+4.

Q: • Create a symmetric equation of a line with the digits 6, 8 and 4. Does the point D (7,-1,8) lie on…

A:

Q: 1. Find the distance between the points P = (-1,3) and Q = (4, -2). Find the midpoint of the line…

A: Consider two points Px1, y1 & Qx2, y2 Then, the distance between the points PQ is given by:…

Q: Plot two points that are both 3 units away from the x-axis and 3 units away from (5, 4). (Hint: Use…

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Q: Find the distance between the points p1and P2. P1 =(3, -4); P2 =(5, 4)

A: We have two points of the form P1x1,y1=3,-4  ,  P2x2,y2=5,4. Distance between two points is…

Q: Find all points having a y-coordinate of - 6 whose distancefrom the point (1, 2) is 17.(a) By using…

A: a. Using Pythagorean theorem. The converse of the Pythagorean Theorem states that the sum of the…

Q: The equation of the line tangnet to the graph of 24e^x at x=2?

A: Find the derivative of the given function.

Q: Find the value of x,if the distance between the points (x,1) and (3,2) is 5

A: Use the distance formula and solve for unknown.

Q: 1. Find the point on the line 1 - a that is closest to the origin.

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Q: find the distance from the point to the line. (3, -1, 4); x = 4 - t, y = 3 + 2t, z = -5 + 3t

A: Given Data The points is 3,-1,4. x=4-t. y=3+2t. z=-5+3t.   The line is passes through the points of…

Q: Find all points having a y-coordinate of - 3 whose distance from the point   (1, 2) is 13.

A: Consider the points are A = (x,-3) and B=(1,2) The distance between A and B is 13 units.   If the…

Q: In the Cartesian plane below, rectangle MNQR is shown. y (cm) N(12,29) M P >x (cm) R • An ant starts…

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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: a) Write down the equation for a line passing through points (2, 1, 4) and (1, 3, 5) b) Use the…

A: a) Write down the equation for a line passing through points (2, 1, 4) and (1, 3, 5)b) Use the…

Q: In this problem we use the Distance Formula. Which of the points A(6,7) or B(-5,8) is closer to the…

A: The two given points are A(6,7) and B(-5,8) To find which point is closer to origin As given…

Q: Find the distance between the points p1and P2.

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Q: Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.…

A: Let A and B are two endpoints of the segment AB. The coordinate of midpoint M is given by the…

Q: In the problem we use the distance formula. Which of the points P(3,1) and Q(-1,3) is closer to the…

A: The distance between the points Q(-1, 3) and R(-1, -1) is:…

Q: A yacht is travelling on a course parallel to and 80 kilometers from the straight shoreline of…

A: Given,         A yacht is traveling on a course parallel to and 80 kilometers from the straight…

Q: To begin deriving the equation of the line y = 2x, Davina drew a triangle with vertices (0, 0), (1,…

A: To find the equation of a line passing through two given points, we need to first join the two…

Q: In the Cartesian plane below, rectangle ABCE is shown. у (km) B C(38,16) >x (km) E A boat starts…

A: Think of it all as a top view of a boat in a lake. and forget about the coordinate axes. At first,…

Q: Use the distance formula to find the distance between the two points: (7,3) and (15,3)

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Q: Find the distance and midpoint between points P(6, -3) and Q (-2, -5)

A: Given points are P(6,-3) ,Q(-2,-5)From middle point formula ,middle point between(x1,y1) and (x2y2)…

Q: The formula for the distance between two points is:

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Q: (a) How do you find the distance from a point to a line?

A: Let the point be And the line be Then the distance d is,

Q: Find the distance between each of the pairs of points.(a) (-1, 5) and (1, -2)(b) (5, 0) and (2, 7)

A: Find the distance between each of the pairs of points.(a) (-1, 5) and (1, -2)(b) (5, 0) and (2, 7)

Q: Find the distance between the given pair of points: 1 and 7

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Q: What is the midpoint of the line segment? Drag the coordinates to the boxes to correctly match the…

A: Topic:- geometry

Q: Find the distance between the following two points: (-1, -2) and (-1, 3)

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Q: What is the distance between the following points? 4- 17 -8-

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Q: Given the pair of points: (0,-5) and (-1,6), a) Find the distance between the two points. b) Find…

A: The pair of points is (0,-5) and (-1,6).

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: find the distance from the point to the line. (-1, 4, 3); x = 10 + 4t, y = -3, z = 4t

A: Given  Point = P (-1, 4, 3) Equation of line : L1 :  x = 10 + 4t, y = -3, z = 4t Rewrite the…

Q: Consider the two points defined as: (1/2,-3) and (-1/6,- 1/2).The distance between the points is:

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Q: --2 4 X

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Q: At what points will the line y = -2x intersect the unit circle x2 +y2 =1 ?

A: The circle equation is x2+y2=1 and the line equation is y=-2x.

Q: Find the distance between each pair of points: c) (-5, 2) and (7, -3) d) (x - 3, y + 2) and (x, y -…

A: The given points 6,4 and 6,-3 formula used: distance between the pointsx1, y1, x2, y2:…

Q: State the formula for the distance between (x1, y1) and (x2, y2).

A: Determine the formula for the distance between x1, y1 & x2, y2

Q: d. (1,1/2), (1/2,-2) e. (2, -4), (0,7) f. (-2.5, -3.5), (6.5, -5.5)

A: We can find the distance using the distance formula as below.

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.