A rectangle has vertices at the points (0,0), (6,0), (6,4), and (0,4) on a coordinate plane as shown.

Q: 3,0 on a coordinate plane

A: we have to plot (3,0) on a coordinate plane using graph we can plot (3,0) on coordinate plane as…

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: Find an equation (in standard form and in general form) of the plane containing the points (2, 1,…

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Q: Find a plane through the points (3,2,3), (4,-3,-3), (4,4,1)

A: The given points are: (3, 2, 3),  (4, -3, -3),  (4, 4, 1)

Q: Find an equation of the plane perpendicular to the line through (2, 2, –4) and (7, –1,3) and…

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Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: A plane is passing through the points A(0,1,3), B(-1,2,0) and C(3,-2,4). Find

A: The vector form of the equation of a plane is given by the expression (r→-a→)·(b→-a→)×(c→-a→)=0.…

Q: Find an equation of the plane that passes through (2, –1, 5) and is parallel to the plane containing…

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Q: two vertices of the a  triangle ABC are (6,-2) and B(4,3) If the co-ordinates of its centroid be…

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Q: Find the equation of a plane through the points (– 8, 2, – 1), ( – 4, – 1, 8), ( – 8, 6, – 6). -

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Q: Find an equation of the plane determined by the points P(0,0,0), Q(-1,2,4), and R(2,1,3)

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Q: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

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Q: Find an equation of the plane that contains all the points that are equidistant from the given…

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Q: Find a plane containing the point (– 3, – 3, 7(t) = (– 2, – 3, – 5) + t(3, 4) and the line 6, 7).

A: we have to find the equation of plane that contains the point (-3,-3,-4)  and the line…

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: Determine the coordinates for the intersection of the diagonals in RSTU with vertices at…

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Q: Find an equation of the plane passing through the three points give P = (4, –1, 2), Q = (1, 1, 1), R…

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Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: Find an equation of the plane consisting of all points that are equidistant from (0, -5, 2) and (-5,…

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Q: In space coordinates system, the y-axis consists of all points of the form O (x, 0, 0) O (0, 0, z) O…

A: we know that(x,y,z) is nothing but distace of a point from origin along the x,y,z-axis

Q: Find the distance between the point (5,-4, 1) and the plane containing the points (4, -2, 3), (-1,…

A: Here we have to find the distance between the point (5,-4,1) and the plane containing the points…

Q: Find the equation of a plane passing through (2,1,3), (3, –1,5), and (1,2, –3).

A: Equation of plane

Q: A cube is located such that its bottom four corners have the coordinates (-4, –5, –1), (-4, –1, –1),…

A: Given a cube is located such that its bottom four corners have the coordinates (-4,-5,-1),…

Q: Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (7,6) ,…

A: Given:

Q: Find the equation of the plane through (-1,6,2) and perpendicular to the join of (1,2,3) and…

A: We have to Find the equation of the plane through (-1,6,2) and perpendicular to the joining of…

Q: Consider a circle C in the xy-plane. If it is given that the points (2, 3),(2, −1) and (0, 3) are on…

A: Given points are (2, 3),(2, −1) and (0, 3)

Q: Determine homogeneous coordinates of the points (3,4) and (1-,7)

A: Homogeneous coordinate:-converting any two dimension coordinate to three dimensional coordinate  (x,…

Q: Find the equation of a plane consisting of all points that are equidistant from (5,5,-1) and…

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Q: 2. Find the equation of the plane through the points (1, -3,2), (3,0,– 1), and (0,5,5).

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Q: plot the given pair on a cartesian plane {(1,1),(2,4),(3,7),(4,10),(5,13)}

A: The given pair of points are  A(1,1), B(2,4), C(3,7), D(4,10), E(5,13)

Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: Find an equation of the plane passing through P = (1, 2, 3), Q = (0, 0, 3), and R = (−2, 5, 4).

A:

Q: 2. Find the equation of the plane through the points (1,–3,2), (3,0,–1), and (0,5,5).

A: The solution is given as follows

Q: :Find the equation of the plane through (-1, 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

A: Given,           The equation of the pane through -1,6,1 and perpendicular to the join            of…

Q: Find the equation of plane with vertices P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

A: We have to find

Q: Find an equation for the plane consisting of all points that are equidistant from the points (-6, 3,…

A:

Q: 2) Do the points (1,0, -1), (0,2,3), (-2,1,1), and (4,2,3) lie in the same plane?

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Q: Find an equation of a plane containing the three points (0, -2, 4), (3, -3, 2), (3, -2, 4) in which…

A: The equation is  :-

Q: Find the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)

A: Given: points (0,1,3), (2,2,2), (3,2,1) Find: equation of the plane containing given points

Q: ( ) Find the point of intersection of the plane passing through the points P(0,-2,-6) P(-1,1,5) and…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the equation of a plane passing through A(2,1,3), B(3, −1,5), and C(1,2, −3).

A:

Q: The triangle with vertices A(0, 1, 2), B(-1,0,2) and C(1,-2,0) has area = (ii)

A: A(0,1,2) B(-1,0,2) C(1,-2,0)

Q: Find the equation of the plane through the points (1, -1, O), (1, 0, 1) and (2, 2, 1).

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Q: The line passes through the point(7, 8, 9) and is parallel to the xz-plane and the yz-plane. 7,8,1 +…

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Q: Find the points at which the line that passes through (–6,6,4) and (12,–6,2) intersects the three…

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Q: Find a plane containing the point (2,-1,3) and the line of intersection of the planes 5x + 7y – 6z =…

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Q: A parallelogram has 2 vertices (1,1) and (0,7) and their diagonals intersect at the point (4,3).…

A: Given:

Q: A trapezoid is a quadrilateral with at least one pair of parallel sides. Show that the quadrilateral…

A: slope of the line joining (x1,y1),(x2,y2)  is y2-y1x2-x1

Q: Consider the triangular region in the plane given by the triangle (1, 6), (6, -1), and (1, -4).…

A: See attached file for a step by step explanation.