Midpoint of a line segment Show that the point with coordinates(x1 + x2 /2 , y1 + y2/2 )is the midpoint of the line segment joining P(x1 , y1) to Q(x2 , y2).

Q: Isosceles trapezoid ABCD is centered at point K. Perpendicular lines m and n intersect at point k.…

A:

Q: The planes with the equations x + 2z = 12 and y – 3z = 6 intersect in a line. Find the equation for…

A: Given: Planes:x+2z=12y−3z=6

Q: Find the plane determined by the intersecting lines. L1 x= - 1 + 3t y =2+4t z=1-t L2 x= 1- 4s y = 1+…

A:

Q: Point C is the midpoint of AB. There exists a point D that is located on AB and is one-third of the…

A:

Q: The planes with the equations x + 3z = 12 and y - 5z = 10 intersect in a line. Find the equation for…

A: The plane equations x+3z=12  and  y-5z=10

Q: Midpoint formula Prove that the midpoint of the line segment joining P(x1. y1- Z,) and Q(x,. Y2, Z,)…

A:

Q: Find a parameterization for the line segment joining points (0,3​) and ​(6​,0) using the angle θ in…

A:

Q: Find a line that intersects the plane x+y+z=4 at only one point

A:

Q: I Point A (-5,8) 1s reflected across thie line y-x. What: are the. Coordinates of A? Show wor lC and…

A:

Q: Suppose you start at the origin, move along the x-axis a distance of 6 units in the positive…

A:

Q: Equation of the plane passing through the point (3, -2, 5) and parallel to yz-plane is Do not leave…

A: The plane passing through the point (3,-2,5) and parallel to yz-plane.

Q: A cariable straight line drawn through the point of intersection of the straight lines x/a+y/b=1 and…

A:

Q: 22.foci F(-9,0), F(9,0) and vertices V,(-13,0),V,(13,0)

A:

Q: Line segment AB is a diameter of the x² +y² + z² - 2z + 8y = 9. Find point B if A = (0, у, 0).

A: To find the point B if Coordinates  of A are given for the sphere.

Q: About family of curves. Draw the curves in one Cartesian plane.

A: We draw the family of equation of the lines y+5=mx-3 for different values of m. [Blue lines] And we…

Q: Find the distance from the point (5, 5, 5) to the line x = 0, y = 5+ t, z = 5+t. Find the point P…

A: Explanation of the answer is as follows

Q: Point P(25,27) lies on line segment AB in the Cartesian plane below. In what ratio does P divide the…

A: The point P(25,27) lies on the line segment AB,  Point A(16,6) and B(31,41) let Point P(25,27)…

Q: Distance from a point to a plane Find the distance from the point (2, 2, 2) to the plane x + 2y + 2z…

A: here given the equation of the plane

Q: Parametric equations for the line containing (3,-1,4) and (-1,5,1) are: O x = 1- t, y = 3 + 6t, z =…

A:

Q: Which geometric construction matches the diagram below?

A: Given-  To Find- Which geometric construction matches the diagram above.

Q: Horizontal plane Q and vertical plane N intersect.

A: Explanation: Here we will draw the two planes Q is horizontal plane & N is vertical plane.

Q: How do you solve for square roots in fractions? Im suppose to solve the midpoint of the line joining…

A: Given formula is M = (x1 + x2)/2

Q: Line A goes through the points (0,3) and (5,-1). Plot another point other than point B with integral…

A:

Q: Find the distance between the point and the line. (Round your answer to four decimal places.) Point…

A: The given equation of the line: y=-7x-6and the given point is 7,-7.We need to find the distance from…

Q: Point ZZ is located at (-5,-3)(−5,−3) on the coordinate plane. Point ZZ is reflected over the…

A:

Q: the xyz-plane determine the distance and angle from point (2,1,1) in the space and two planes…

A: The distance between point Px1,y1,z1 and the plane Ax+By+Cz+D=0 is  d=Ax1+By1+Cz1+DA2+B2+C2

Q: QI/ Determine whether the two planes are parallel or intersecting. Find their line of intersection…

A:

Q: Find the distance between the point and the line. (Round your answer to four decimal places.) Point…

A:

Q: QI) Find equations of the Normal plane and Osculating plane of the curve x = 2 sin 3t, y = 2t, z =…

A: Givenx=2sin3t , y=2t , z=-2cos3tPoints(0,π,-2)To findEquation of normal plane and osculating plane

Q: 3: One way to try to determine the line of intersection of two planes in 3-space is to find two…

A: The Geometric Idea behind the method is as follows: By putting on dimension equal to zero, the…

Q: The line = (2, -1, -2) + s(1, 1, -2), sER, intersects the xz-plane at point P and the xy-plane at…

A:

Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Find equations for the line of…

A: Given equation of planes - 3x+6z = 1                ........................(1)2x+2y-z = 3…

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-9,0,…

A:

Q: The line through the point (0, 14, – 10) and parallel to the line x= -1 + 21, y = 6 – 31, z = 3 + 9t…

A: If the line is parallel to the line x = -1 + 2t; y=6 -3t and z=3 + 9t, then the line is parallel to…

Q: Parametric equations for the line through (5, 3, 7) and parallel to the line x = 3−t, y = 2, z = 8 +…

A: Known fact: The equation of line passing through x1, y1, z1 and parallel to the line x=x2+at,…

Q: 17. projection of the line Find the equation of the 3x-y + 2z-1=0 = x +2y-z-2 on the plane 3x +2y +…

A:

Q: prmal line of

A:

Q: Line t contains the points (5, 2) and (-2,-3). Plot a point other than point P with integral…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Parameterize the curve of intersection of the surfaces so that the direction is clockwise when…

A: Note: According to our guidelines We’ll answer one of the question since the exact one wasn’t…

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (- 5,…

A:

Q: oints. Assume all the lines are non-vertical. 81. (2а, а) and (За, -а)

A:

Q: QI) Find equations of the Normal plane and Osculating plane of the curve x = 2 sin 3t, y= 2t, z=…

A: Given, r(t0)=0, π, -2. Since r(t)=xt, yt, zt. Therefore, r(t)=2sin 3t, 2t, -2cos3t. First, find the…

Q: Use a graphing utility to sketch the intersecting graphs of the equations and determine whether or…

A: topic- equations and their slopes

Q: Find the coordinates of the point. The point is located in the yz-plane, seven units to the right…

A:

Q: Three intersecting planes Describe the set of all points (if any) at which all three planes x + 3z =…

A: Consider the planes, The objective is to describe the set of all points at which all above three…

Q: Equation of the plane that passes through the point (8, -6, 4) and contains the line of the given…

A:

Q: Equation of the plane passing through the point (3, –2, 5) and parallel to yz-plane is

A:

Q: rdinate plane What coordinate represents the midpoint of segment PQ

A: Co-ordinate of P(8,-7) and Q(-6,-3) co-ordinate of mid-point of (x1,y1) and (x2,y2) is…

Q: Using analytical method prove that the mid - point of the hypotenuse of a right angled triangle is…

A:

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-8, 0,…

A:

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.