7. Let ABCD be a parallelogram in the affine plane. Prove that the line connecting the midpoints of two opposite sides passes through the point where the diagonals intersect.

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: what are the coordinates of the point on the directed line segment from (-6,-1) to (6,-9) that…

A:

Q: Let the line DE be a line parallel to the base BC of triangle ABC. Show that if the line AF divides…

A: Given,DE∥BCAF bisects BCLet intersection of AF with DE be 'x'

Q: What are the coordinates of the point on the directed line segment from (-4,-9) to (1,1) that…

A: This question is related to line. We will solve this question by using section formula.

Q: Find the point E that partitions the directed segment CD  in a ratio of 1:5, given the points…

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Q: 9. Prove, by coordinate geometry that QRST is a parallelogram. Q(0

A:

Q: What are the coordinates of the point on the directed line segment from (-1, -9) to (2, 6) that…

A: Use the section formula and simplify.

Q: A quadrilateral is defined as a parallelogram if it has two pairs of parallel sides. True O False

A: Using property of parallelogram,

Q: Given quadrilateral WXYZ with coordinates W(4, 5), X(9, 4), Y (8,0) and Z(3, 1). Prove or disprove…

A: Quadrilateral is parallelogram if diagonals bisect each other

Q: Let points A; B , C , and D in R3 have respective coordinates (1, 2, 3), (−2, 3, 5), (0, 3, 6), and…

A: Given: A(1, 2, 3), B(−2, 3, 5), C(0, 3, 6), D(3, 2, 4)

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: A(-3, 2), В(5, — 4), С(7, 7)

A: Consider the given points,  Now, prove that C is on the perpendicular bisector of segment…

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

A: Consider the given vertices A-3,2, B5,-4, and C7,7. If C is on the perpendicular bisector of AB,…

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: Can you determine if there’s enough info to prove the m is parallel to n? If so, which theorem would…

A:

Q: let ABCD be a reactangle.The perpendicular bisector of line segment BD intersects line AB and BC in…

A: In this rectangle ABCD the perpendicular bisector of diagonal BD is EF and EF will be AC.

Q: Suppose that a box has its faces parallel to the coordinate planes and the points (4, 2,−2) and (−6,…

A:

Q: Let ABCD be a rectangle. The perpendicular bisector of line segment BD intersects lines AB and BC in…

A: Draw the diagram as shown below : Calculate the cordinates of L .L=a+02,b+02=a2,b2Calculate of…

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

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: 2. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at…

A:

Q: Consider a quadrilateral with vertices D(0, 0), J(5, 5), N(8, 4), and G(7, 1). Determine the most…

A: We have to draw the given quadrilateral also find the type.

Q: The vertices of quadrilateral KAIT are K(0,0), A(a, 0), I(a + b, c), and T(b, c). Use coordinate…

A: Parallelogram is a kind of quadrilateral with two pairs of opposite sides. In a parallelogram, the…

Q: (5) Prove that in an Isosceles triangle, the angle bisector at the apex angle is also the median and…

A:

Q: What is the locus of points in space equidistant from two parallel planes?

A: Locus: If the two lines are in Rn the points equidistant from them form an n−1 dimensional…

Q: Prove that all the points on a perpendicular bisector of a line segment AB are equidistant from the…

A: Statement:All the points on a perpendicular bisector of a line segment AB are equidistant from the…

Q: Verify that the points A(0, 3, 2), B(1, 5, 5), C(6, 9, 5), D(5, 7, 2) are the vertices of a…

A: Given points are A(0,3,2), B(1,5,5), C(6,9,5), D(5,7,2).

Q: Prove without using the concept of duality: In the four-line geometry, there exists a pair of points…

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Q: Suppose that four lines in a given plane a1, a2, b1. bz are given, with the conditions (also given)…

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Q: Prove that there exists a set of two lines containing all the points of the geometry.

A:

Q: Let A, be the center of the square inscribed in acute triangle ABC with two vertice side BC (as…

A:

Q: What are the coordinates of the point on the directed line segment from (3, 3) to (10,-4) that…

A: General formula

Q: Prove that a parallelogram is a rhombus, a parallelogram with four equal sides, if and only if its…

A: Given : ABCD is a parallelogram              AB≅BC              AC⊥BD Prove : ABCD is a rhombus

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: Let ABCD be a rectangle. The perpendicular bisector of line segment BD intersects lines AB and BC in…

A: We need to prove FM and EN are perpendicular.

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: 14. How many straight lines can be formed by joining 12 points on a plane out of which no points are…

A:

Q: Prove analytically that in any triangle the perpendiculars drawn from the vertices upon the opposite…

A: Given-  the perpendiculars drawn from the vertices upon the opposite sides. To prove-the altitudes…

Q: What point divides the directed line segment AB into a 2:3 4. ratio? 3- -2- 456 89 10 11 12 13 14 15…

A:

Q: 14 12 10 PARK 4. 2. 2. 10 12 14 00

A: By using the opposite sides parallel and conjugate theorem we show that the polygon which represent…

Q: Show that quadrilateral RSTV with vertices R(- 5, - 3), S(1, – 11), T(7, -6), and V(1, 2) is a…

A: Solution: Consider the given that RSTV has vertices R(-5, -3) , S(1, -11), T(7, -6), and V(1, 2)…

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

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Q: Prove that the line joining the midpoint of a median to a vertex of the triangle trisects the side…

A: Here ask to prove the line joining the midpoint of a median to a vertex of the triangle trisectsthe…

Q: 2. Find the area of the parallelogram whose vertices are given by: P: (1,2, –1), P2 = (4, 2, -3), P3…

A:

Q: Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1) and M(-1, 2) is a square. 10 4…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: What are the coordinates of the point on the directed line segment from (-1, –2) to (9, –10) that…

A:

Q: What are the coordinates of the point on the directed line segment from (-1,-10) to (7,6) that…

A: To find the coordinates point.

Q: A diagonal may be inserted onto a diagram of a parallelogram to complete a proof involving the…

A: A parallelogram is a closed figure with 2 pairs of opposite sides parallel to each other.