Plot two points that are both 3 units away from the x-axis and 3 units away from (5, 4). (Hint: Use the distance formula to set up an equation!) (5,4) C- (x,3) 3 3 (x,0)

Q: Find the equation of the line that passes through the point (-2,1,1) and that is parallel to the…

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Q: B. Find the point on the line y = 3x that is closest to the point (50, 0).

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Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

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

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Q: Determine the point(s) on y=x2-1 that are closest the point (7,7)

A: Let (x, y) be the point on the given graph which is closest to (7, 7). Therefore the distance…

Q: Find the distance between the points (i) P(-6,7) and Q(-1,-5) (ii)R(a+b,a-b) and S(a-b,a-b)

A: Use distance  formula

Q: Find the length of the curve. x = y^2/3, 1 … y … 8

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Q: Find the shortest distance from the point x = (-3, 0, -12)  to the line r = t(0, -2, -2).

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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: 4. Find the distance between the two points S(-5,-2) and T(-3,4).

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Q: Find the equation of the line through (4/3, -2) parallel to the y axis. O a. 3x-4 O b. 3y--4 -3x-D4…

A: Let's find.

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: 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: In the coordinate plane, right triangle AXYZ is reflected over the line y = x. 5 3 X 2- -6 -5 -4 -3…

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Q: b) Determine the equation of the line that goes through the point (-1,2) and crosses the positive x-…

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Q: Find the distance from the point to the line. Knowing that the point Po (2, 1, 3), x= 2+2t, y= 1+6t,…

A: The distance of a point P from a line passing through the point Q and parallel to the vector v→ is…

Q: 9. Find a point on the y-axis which is equidistant from the point A (6,5) and B (-4,3).

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Q: is an equation of the line that passes through the point (-2, 7) and is endicular to the line x-4y =…

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

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Q: find an equation of a line that passes through the point (-1,8) and is parralel to 3x+4(y-1)=3 and…

A: Line 1 is given as,

Q: find all points on the y-axis that are a distance of 6 from the point (3,-1)

A: Let the point is (0,y).

Q: Find the points on x=3-y^2 that are closest to the given point (1,0)

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

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Q: Used to determine the distance between two points (*11) and (*, V2) d= V(*-*)2 +(2 -1)2 and (X2 d%3D…

A: Given that distance between points                                                 (x1, y1)  &…

Q: Find the distance from the point to the line.   (−4,4,−1)​; x=-3+3t, y=-1+t, z=1+2t   The distance…

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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: The equation of the curve passing through the point (2, 3) and having slope 6x^2 - 8x + 1 at every…

A: Solution is given below:

Q: The point that is symmetric with respect to the y-axis to the point ( - 2, 5) is__________

A: It is known that the graph of y=fx is symmetric with respect to y-axis means f-x=fx=y.

Q: Find the line L passes through the point (-2.2) and perpendicular to the line L': 2r+y 4.

A: Given : The line L passes through the point -2,2

Q: Find the distance from the point (4, 3, 0) to the x-axis

A: To find the distance from the point (4, 3, 0) to the x-axis

Q: B) Find Duf of f(x,y.z) x + y? + 2? - 3 at point(1,1,1)in the direction of point (3,5,-3).

A: Take gradient at given point and take dot product with unit vector for directional derivative

Q: roblem 4.1 Find the point on the line y = 2x + 3 that is closest to the origin.

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Q: Find an equation of the line perpendicular to 3x - 2y = 7that contains the point 11, 52.

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Q: 4. A (-3, 1) 5. P(4,-3) and М(2, 2) Q(-1,4) and

A: The points are:4) A-3, 1 and M2, 25) P4, -3 and Q-1, 4To find the distance between them.

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: Find a point on the line y = 2x 3 that is 5 units from the x axis. %3D

A: The given equation is, y=2x-3

Q: Find the point on the x-axis that is equidistant from the points (1, 2) and (2, 3). The coordinates…

A: soln:point on x-axis which is equidistant from the points 1,2 and 2,3

Q: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

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Q: Find the point of inflection of the curve x3 – 6x2 + 2x + 14.   a. (-1,-4) b. (2,2) c. (1,4) d.…

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Q: How do you compute |PQ| from the coordinates of the points P and Q?

A: Suppose the coordinates of P and Q  are given as, a,b and c,d. Then to compute PQ⇀,   PQ⇀=c-a2+d-b2…

Q: Find an equation for the set of all points (r, y, z) equidistant from point 10.) (1,0, 2) and the…

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Q: Find the equation of the line that 2 is perpendicular to y = -x and contains the point (4,-8). %3D 3

A: If two lines are perpendicular then the product of their slopes is -1. The required line is…

Q: Find the approx. distance of the point (6, -3) from the line 2x – y +4 = 0 a. 6.5 units O b. 10.5…

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Q: Q2: The distance between the point (1, -3) and (4, 5) is

A: The given points are (1, -3) and (4, 5).

Q: 19. What is the equation in slope-intercept form for the line parallel to y = -3x + 9 that contains…

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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: 5- Find the distance from the point to the line. a. (0,0, 12); x = 4t, y = -2t, z = 2t b. (0, 0, 0);…

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

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Q: An object is traveling along a path described by y =x +3. Where along that path will the object be…

A: Given: An object is travelling along a path described by y=x+3.

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.