In a field plane PG(2, F), a line ax+by+cz = 0, not through the vertices of the triangle of reference ABC, intersects the sides BC, CA, AB in the points X, Y, Z, respectively. Let P = YBn ZC, Q = ZCn XA, and R = XANYB. Show that AP, BQ, and CR are concurrent, and find the coordinates of the point of concurrency.

Q: Show that the lines 2r + 3y = 1 and 6r - 4y -1=0 are perpendicular.

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Q: Let c1= ((c1x,c1y), r1) and c2= ((c2x,c2y) , r2) be two circles and p = (px,py) be a point. Decide…

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Q: The Theorem of Pappus states that if A,B,C are three distinct points on one line and if A',B',C' are…

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Q: 30) The coordinates of the endpoints of line segment CD are C(–4, 1) and D(3, 4). Reflect the line…

A: x-axis is also known as the principal axis . The y-coordinate of the point that lies on x-axis is 0.

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A: Since plane passes through the given points therefore

Q: 1.) Find the slope and angle of the line joining (2, 2) and (22) that the three points (x,-3), (9,…

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Q: . For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line = (2,-1,-2) + t(3,1,-2)…

A: I have appended the formula used in the solution part of the question

Q: the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axes at concyclic points,then prove that…

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Q: Do the points (0.5, 1), (1, 1.2), (2, 2) lie on a line?

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Q: 14) Write the equation of the perpendicular bisector of segment QR if Q(3, -2) and R(7, 6)

A: Find the equation

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Q: It is possible for two intersecting lines to be noncoplanar.

A: It is possible for two intersecting lines to be noncoplanar.

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Q: Find the vertices of the triangle whose sides are the lines x = 0, x + y + z = 0, and 3x - 4y + 5z =…

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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: Are AB and PQ parallel, and if so, do they paint in the same dırecton? A= (4,4) B= (-S, 2) P= (0,-1)…

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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.

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Q: → → If m= (2. 1. 5) and n = (3. 0. x) are perpendicular, then the value of x is

A: Solve the following

Q: If the lines a₁x + b₁y+C₁ = 0 and a₂x + b₂y + C₂ = 0 cut the coordinate axes at concyclic points,…

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Q: Find the value of X such that and are perpendicular

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Q: 1.) Line D has the equation y = -2/5x + 3 and line G has the equation y = -2/5x + 1. Lines D and G…

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Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…