Prove that the midpoint of the hypotenuse of any right triangle is equidistant from the vertices. (Hint: Label the vertices of the triangle O(0, 0), A(a, 0), and B(0, b).)

Q: Show that the triangle with vertices P(6, ; 7), Q(11, ; 3) and R(2, ; 2) is a right -angled triangle…

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Q: - The cuboid (right) has one of its corners removed to leave a flat triangle BDC. Calculate: a…

A: We draw lines as shown in the figure below Here lines XC and HG are parallel and equal. So XC = 5…

Q: A__________ _____________is a positive angle whose vertex is at the center of a circle.

A: A __________ _____________ is a positive angle whose vertex is at the center of a circle.

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: For proving the theorem "The midpoint of the hypotenuse of a right triangle is equidistant from all…

A: It is possible to prove the theorem for any triangle whatsoever, but from the point of view of this…

Q: Line AB is formed by the vertices A (1, 2, -2) and B (-1, 0, 2). If C is the midpoint of AB, find…

A: Given,  the coordinates of A and B which forms line AB  And c is the mid point is AB Hence the…

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

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Q: Given that the points A(-3,3),B(2,-4),C(9,-9),and D(4,-2) are vertices of the rhombus ABCD find the…

A: We have to find the coordinates of the point of intersection of its two diagonals

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…

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Q: (b) Prove that the perpendicular bisector of a chord of a circle passes through the centre.

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Q: Show that in hyperbolic geometry, the vertices of a triangle can belong to the same circumference.

A: Hyperbolic geometry comes into consideration when surfaces are curved not like surface of a room or…

Q: 1. The vertices of quadrilateral ABCD are A(-2,3), B(4,6), C(10,3), and D(0,-2). Use coordinate…

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Q: Without plotting the points or drawing the figure, find the coordinates of the new vertices of the…

A: given pentagon with vertices at V(3,2), W(5,10), X(6,12), Y(−0.5,1.25), Z(1,0)

Q: Show that A(-3, 1), B(1, -1), C(4, 1), and D(3, 5) are vertices of a trapezoid.

A: Given vertices are A-3,1, B1,-1, C4,1 and D3,5. To show the vertices are of a trapezoid. Solution:…

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: Show that the points A = (3, 4), B = (1, 1), and C = ( - 2, 3) are the vertices of an isosceles…

A: Given: Points are A = (3, 4), B = (1, 1), and C = ( - 2, 3)

Q: 2. What are the coordinates of the fourth vertex C so that rectangle ABCD is formed? Bty (-1,6) 81y…

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Q: A rectangle ABCD which measures 18 centimeters by 24 centimeters is folded once perpendicular to…

A: SOLUTION: Let ∠DCA=θ; tanθ=18/24=3/4 AC=18^2+24^2=30 Length of crease = AC*tanθ=30*(3/4)=22.5…

Q: Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is…

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Q: Show that the triangle with vertices A(0, 0), B(1, √2), andC(2, 0) is equilateral.

A: An equilateral triangle is a triangle in which all sides are equal, and consequently, all angles are…

Q: Graph the image of square ABCD after a reflection across the y-axis. 10 4 2. -10 -8- -4 0. 4. 6. 8.…

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Q: What will be the new coordinates of the triangle with vertices A(0,1),B(1,2) and C(1,0) when : i) it…

A: given coordinates of a traingle ABC A(0,1),B(1,2) and C(1,0) what will be the new coordinates of…

Q: Which of the following is four-point geometry?

A: Axioms of Four Point geometry is given as 1.   There are exactly four distinct points 2.   Any two…

Q: In the context of hyperbolic geometry, show that the segment joining the midpoints of two sides of a…

A: Given below clear explanation

Q: A parabola is the locus of a point equidistant from?

A: Answer : A parabola is the locus of a point equidistant from a fixed point and a fixed line.

Q: What is the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4,0), C(5,4), and…

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Q: Consider the triangle ABC with vertices A(0,2), B(2,0), C(/2, v2) Also, Find the vertices of the…

A: The triangle ABC with vertices A(0,2), B(2,0), C(2,2)The dilating factor of 3 about origin.

Q: Prove that the midpoint of the hypotenuse of a right triangle is. equidistant from the verticle

A: Instead of T,S,V and M I choose C,A,B and D

Q: Is of quadrilateral QRST intersect at P(-3,3). QRST has vertices at Q(4,7) and R(-4,5). What must be…

A:

Q: 10. What is the midpoint of the longest side of the triangle with vertices A(1, 4), B(3, 4) and C(3,…

A: first we will draw the triangle then find the mid point of the larger side

Q: Prove that the diagonals of any parallelogram bisect each other. (Hint: Label three of the vertices…

A: Given:- ABCD is a parallelogramTo prove:-AO=CO                 DO=BOProof:-In ∆AOD and ∆COB∡OAD=∡OCB…

Q: If two vertices of an equilateral triangle are at (0, 0) and (2a, 0), what point is the third…

A: Two vertices of equivalent triangle are 0, 0  and  2a, 0. Clearly, the distance between 0, 0  and…

Q: Is a square always a rhombus

A: Squares and rhombus

Q: Show that the triangle with vertices A(0, 0), B(1, √3), and C(2, 0) is equilateral.

A:

Q: prove that if A is a point on the perpendicular bisector of line segment B-C  then A is the same…

A: Prove that if A is a point on the perpendicular bisector of line segment B-C  then A is the same…

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: Prove analytically that the midpoint of the hypotenuse of a right triangle is equidistant from the…

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Q: Determine ξ so that the points P1(4, −3), P2(ξ, −8), and P3(12, −21) are the vertices of a right…

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Q: Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a…

A: Given that: (1, 5), (6, 10), (0, 16)

Q: 2. Show that diagonals of quadrilateral CUTE are congruent for C(5,-1), U(9,-1), T(9,0) and E(5,0).…

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Q: (1) Riley plotted A(-1,6), B(3,8), C(6,-1), and D(1,0) to form a quadrilateral. Prove that Riley's…

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Q: Show that if a line is drawn from the vertex of an isosceles triangle that bisects the base of the…

A: Let ABC is an isosceles triangle such that AB=AC. Let AD is the bisector of angle A. To prove BD=BC…

Q: Consider the quadrilateral with vertices at A(0, 0), B(a, 0), C(b, c), and D(d, c). Explain why ABCD…

A: Trapezoid: Trapezoids are quadrilaterals which have two parallel sides and two non-parallel sides.…

Q: The vertices of a quadrilateral are G(4, - 1), O(0, 0), L(2, 6), and D(6, 5). Show that…

A: Given: The vertices of a quadrilateral GOLD          G4,-1O0,0L2,6D6,5…

Q: The _____ of a triangle intersect in a point that is equi-distant from the vertices of the triangle

A: The circumcenter of a triangle intersect in a point that is equidistant from the vertices of the…

Q: What is the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(3, 4), C(6, 0), and…

A: We can answer the question as below.

Q: 1. Prove that A(-3; 2), B(1; -6) and C(1; 2) are the vertices of a right-angled triangle a. By…

A: As per bartleby answering guidelines, we are supposed to answer only one question at a time. In case…

Q: Write an indirect proof. 7. Given: mZ1 + mL2 Prove: AABC is not an isosceles triangle with vertex B.

A: The solution is :

Q: Which of the following is a three-point geometry?

A: Three point geometry is a finite geometry subject to the following four axioms: 1) There exist…