Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1) and M(-1, 2) is a square. 10 4 TOX 1 -2 -3 -4 -5 -7 -8

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.

A: 1) Opposite sides are equal , 2) The diagonals of a rectangle are equal.  Distance formula of point…

Q: Q2: The plane is divided into a finite number of regions by drawing infinite straight lines in an…

A: Let n denote number of lines drawn on plane. We will prove the result with the help of mathematical…

Q: The vertices of quadrilateral JOHN are J(-3,1), O(3,3), H(5,7), and N(-1,5). Use coordinate geometry…

A: We are given the vertices J(-3, 1), O(3, 3), H(5, 7), and N(-1, 5). Let us plot the graph first.

Q: A quadrilateral has coordinates R(-5,2),S(-1,3), T(-2,–1) and U(-6,– 2). Verify algebraically, that…

A: Let X be mid point of R(-5,2) and S(-1,3) ∴Coordinate of X is -5-12,2+32…

Q: Prove that quadrilateral ABCD with the vertices A(2,1), B(1,3), C(-5,0), and D(-4,-2) is a…

A:

Q: Use slopes to show that the square with vertices at (-2, 5)9, (4, 5), (4, -1), and (-2, -1) has…

A: To show: The diagonals of the square are perpendicular to each other. Given: The vertices of square…

Q: 5A. In quadrilateral ABCD, ∠B=∠D, ∠B= (2x+5)°, ∠A=3x and x=35°, prove that ABCD is a parallelogram.

A: We need to prove that ABCD is parallelogram.

Q: 3. Quadrilateral QUAD with vertices Q(-4, 2), U(-2, 1), A(O, -2), and D(-5, -4); 90°…

A: Given vertices of the quadrilateral, QUAD are  Q=-4,2U=-2,1A=0,-2D=-5,-4 The quadrilateral is being…

Q: Rectangle MNOP with vertices M(-7,1), N(-4,1), O(-4,-4), and P(-7,-4) in the line y=-x

A: Transform the given rectangle over the line y=-x.

Q: 14a. Show that quadrilateral ABCD is a parallelogram Given A(2, 0) * B * (3, 4) , C(- 2, 6) and D(-…

A: Explanation of the solution is given below...

Q: Which of the following would show that the diagonals of quadrilateral JKLM on the coordinate plane…

A: The given triangle JKLM is,

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.…

A:

Q: 6. Show that the diagonals of the square with the given vertices are congruent perpendicular…

A: The formula for the midpoints of (x1,y1) and (x2,y2) is x2+x12,  y2+y12 and the formula for the…

Q: Show algebraically that quadrilateral WXYZ is a parallelogram. W(-5, -2), X(-3, 3), Y(3, 5), Z(1, 0)…

A: Distance formula: you can use this formula to find the distance between the two points.

Q: 10. Prove that quadrilateral A(1,-2), B(13,4), C(6,8) and D(-2,4) is a trapezoid, but is NOT an…

A:

Q: Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1), and M(-1,2) is a square.

A: We have to prove that the quadrilateral given is a Square

Q: 2) Find the area of triangular ABC of points (4,6,12), (2,7,6) and (-2,5,6).

A: From the given data:

Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3), C(5, 6), and D(2, 1): (x, y)- (x+2, y-6)

A: In Rhombus, A=(-3,-2)B=(0,3)C=(5,6)D=(2,1)

Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle

A:

Q: Prove that the diagonals of a rectangle are of equal length. [Hint: Take the vertices of the…

A: To prove that diagonals of a rectangle are if equal length.  Consider a rectangle which has one…

Q: 2. Show that the points A(2,2,2), B(2,0,1), C(4, 1, – 1) and D(4, 3,0) are coplanar and that they…

A: The solution are next step

Q: 7. If the coordinates of quadrilateral ABCD are A(3, 5), B(7, 6), C(6, 2) and D(2, 1), proveABCD is…

A: Given: Quadrilateral ABCD with vertices A(3,5), B(7,6), C(6,2), D(2,1)

Q: Show that the points (−1, 0), (3, 0), (1, 2), and (1, −2) are vertices of a square.

A: Let us consider A(-1,0) , B(3,0), C(1,2) and D(1,-2) To verify ABCD as a square We need to verify if…

Q: Prove that C is on the perpendicular bisector of segment AB.

A: Solution:Given A(-4,-3), B(6,1) and C (5,-11)To Prove: C is perpendicular bisector of ABi.e., to…

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(5, -2,…

A:

Q: A quadrilateral has vertices A = (0, 0), B = (2,4), C = (0,5), and D = (-2, 1). Prove ABCD is a…

A:

Q: prove that points are collinear 3. P(-15,10), Q(0,-20), R(-10,0)

A: Given ; The points are P(-15,10), Q(0,-20), R(-10,0) .

Q: Show that A(-4, 2), B(1, 4), C(3, -1), and D(-2, -3) are vertices of a square.

A:

Q: Prove that a parallelogram is a rectangle if and only if its diagonals are equal in length. (This…

A: Let ABCD be a parallelogram. Given AC and BD are diagonals of parallelogram in equal length. In…

Q: 6. Prove that quadrilateral LEAP with the vertices L(-3,1), E(2,6), A(9,5) and P(4,0) is a…

A:

Q: :Prove that (4,-1).(6,0).(7,2)and (5,1) are the vertices of a rhombus.Is it a square?

A: In a square the sides are perpendicular but in a rhombus they need not be. All sides are of equal…

Q: 2 Prove that a quadrilateral with the vertices A(-2,3), B(2,6), C(7,6) and D(3,3) is a rhombus. IB

A:

Q: Show that the point P(3, 1, 2) is equidistant from the points A(2, -1, 3) and B(4, 3, 1).

A: Let the distance between P(3, 1, 2) and A(2, -1, 3) be d1 and the distance between P(3, 1, 2) and…

Q: A "rotated" square is placed on a coordinate plane and two adjacent corners of the square are…

A: We will find the length of square as following.

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

A:

Q: Prove that quadrilateral DAVE with the vertices D(2,1), A(6,-2), V(10,1), and E(6,4) is a mbus. Yt…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: quadrilateral

A:

Q: 5. Extension: Find the coordinates of the intersection of the diagonals of the parallelogram with…

A: To find the coordinates of the intersection of the diagonals of the parallelogram with vertices…

Q: 6. Rectangle TUVW with verfices N-3,-1), UO,-2). M(-2,-8), and W(-5,-7): 90° counterclockwise

A: Given points T−3,−1,U0,−2,V−2,−8,and W−5,−7 Concept:when coordinatex,yrotated about 90°…

Q: Prove that the quadrilateral with vertices A(0,0), B(4,3), C(7,-1) and D(3,-4) is a square.

A: →In a quadrilateral, if all sides are equal then quadrilateral is a square. →Calculate the length of…

Q: For any cyclic quadrilateral, the product of the diagonals equals the sum of the products of the…

A: Here we have to determine the name of the theorem. The given theorem is: For any cyclic…

Q: 1. Prove analytically that the lines joining the midpoints of the adjacent sides of the…

A:

Q: help!! the assignment is on quadrilaterals, similar triangles, and circles! I really need this…

A:

Q: 11. a) Show that the diagonals of a quadrilateral with vertices P(-5, -8), Q(-9, -2), R(-3, 2) and…

A: Plot the point on the graph and analyse the figure

Q: Prove that quadrilateral A(1,-2) B(13,4) C(6,8) D(-2,4) is a trapezoid, but is NOT an isosceles…

A: Given the quadrilateral vertices are A(1,-2) B(13,4) C(6,8) D(-2,4) To prove that, given vertices…

Q: Quadrilateral PQRS has vertices P(-4, 2), Q(0, 8), R(3, 6) and S(-1,0). Prove that PQRS is a…

A: join all coordinates  Properties of Rectangle: Opposite sides are equal and its diagonal are equal.

Q: Show that the quadrilateral having vertices at (1, 1,3), (-2,1,-1), (-5,4, 0), and (-8, 4,-4) is a…

A: This is a problem related to area of the parallelogram by cross products. Based on the general…

Q: A quadrilateral has vertices A = (0, 0), B= (2,4), C = (0,5), and D = (-2, 1). Prove ABCD is a…

A: Given :

Q: The vertices of quadrilateral PQRS form a square P(0, 0), Q(4, 3), R(7, -1) and S(3, -4). Use…

A: locating the points on the graph we get

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.