1. The points P, (1,2,3), P₂ (2, 1, 2), P, (3, 0, 1), P4 (5, 2,7) are the vertices of a plane quadrilateral find the Coordinates of the midpoints of the sides. What kind of quadrila- teral do these four mid paints form? 2. Given the set S= {(x, y, z): x² + y² +2² = 1}.] L Find the points of SAL where I is the line passing through the origin and having direction numbers 2, 1,3 3. Determine whether or not the three given points lie on a line A (3, 1,0), B (2,2,2), C (0,4,6)

Q: 1. If (0, 0), (3, 0) and (x, y) are the vertices of an equilateral triangle, find x and y.

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Q: In the diagram below, L(-5; -2), M(-1; -6) and K(5; 4) are the vertices of AKLM in a Cartesian…

A: Let's find.

Q: 15. What is the ordered pair that best represents S on the coordinate plane below? (TEKS 6.11A, RC3,…

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

Q: .Find the equation and sketch the plane that contains the points (2, 6, 1), (-4, 9, -1) and (4, 3,…

A: Equation of plane is 3x+2y+6z = 12

Q: 20. Determine the angle between a = (5, 3, 0) and b = (-1, 0, 8) 21. The vertices of a quadrilateral…

A: Step 1: In order to determine the angle between a=(5,3,0)&b=(−1,0,8) lets use the dot product…

Q: Q6. Let O(0,0), A(1,0), B(1,4) be points in the plane R². Then the following point lies in the…

A: I am attaching image so that you understand each and every step.

Q: a) What is the equation of the line parallel to LM passing through N with point(X1,Y1). b) Show…

A:

Q: a) Explain fully, atleast three possible relationships between two lines in R3 [c3] b) Which of the…

A: (a) The relationship between any two lines in ℝ3 is always one of the following three: They can be…

Q: The points A, B, C and D represent the numbers Z₁, Z2, Z3 and z4 and O is the origin. 9 (a) If OABC…

A: We have to find value of Z3

Q: Use slopes to show that the points are vertices of the specified polygon

A: Given points are A(2,3), B(5,-1), C(0,-6), D(-6,2)

Q: two bees leaving an area in a straight path. Bee's 1 path: r1(t) = + t and Bee's 2 path: r2(s) =…

A: As per the question we are given the trajectory of two Bees and we have to find :whether their…

Q: For the convex set C = {(z,9)+ 13 y.0 < 2.0 < y } (a) Which points are vertices of C? (52/9,35/9)…

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Q: 2. The x- and y-axes divide the coordinate plane into four regions called

A: Given: The x and y axes divide the coordinate plane into four regions

Q: 5. The vertices of parallelogram ABCD are: A(3, -2, 4), B(-2, 0, 5), C(3, -5, -4) & D(x, y, z). a)…

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Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

A:

Q: 33. Sketch the diagram that you would use to find the magnitude of the sum of a and b if the angle…

A: 20. To find the angle between two vectors \(\vec{a}\) and \(\vec{b}\), you can use the formula…

Q: A.If angle ABC has vertices A(3,6) B(-2,-3) and C(8,6) what would the coordinates under the…

A:

Q: iven the points A(2,6,0) and B(3,5,6) determine the point of intersection of this line to x-z plane.

A: Given points are A(2,6,0) and B(3,5,6) The line joining points (x1, y1, z1) and (x2, y2, z2) have…

Q: 6) Consider the three points in the plane given by their coordinates: A = (0,0) B=(2,2) C=(3,5).…

A: I have explained everything with in the solution. Please go through that

Q: Sketch the following points in space three, A (4,5,3); B (1,7,4) and C (2,4,6). Prove that point A,…

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Q: b) Determine the gradient of each side of the triangle c) Using your answers in a) and b), justify…

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Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: 4) The coordinates of the vertices of triangle SUE are S(-2,-4, Y(2,-1), and E(8,-9). Using…

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Q: Represent two planes that intersect at a line represented by 3 +2

A: There are so many pair of planes that represents the same line.