If A = (5, 1), B = (1,-3) and C= (2,-4), find the cosine of 2CAB. Let A = (-3, 2), B = (1, 0) and C= (4, 6) be points in the plane. Prove that AABC is a right-angled triangle.

Q: If the rectangular coordinates of a point are (4,-6) the point symmetric to it with respect to the…

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Q: Find the equation of the perpendicular bisector of side of the triangle having vertices…

A: Slope of a line passing through two points x1,y1,x2,y2 is given by Y2-x1x2-x1 Midpoint of two points…

Q: The midpoint of AB is M (5, –5). If the coordinates of A are (3, –6), what are the coordinates of B?

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Q: Show that the triangle with vertices (5, 4, −1), (3, 6, −1), and (3, 4, 1) is equilateral.

A: To show that the triangle with vertices 5, 4, -1, 3, 6, -1 and 3, 4, 1 is equilateral. Solution: Let…

Q: The midpoint of AB is at (-5,2). If A=(−8,6)), find B.

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Q: The midpoint of AB is M(-1, -5). If the coordinates of A are (3, –8), what are the coordinates of B?

A: A detailed solution is given below

Q: If quadrilateral ABCD was rotated 270 degrees counterclockwise about point D, what would be the…

A: Use coni method to find the rotation of point B after 270 degree rotation, zB'-zDzB-zD=cosθ+isinθ…

Q: Determine if the points X(26, 24), Y(2, 22), and Z(0, 5) form the vertices of a right triangle.

A: Given points are X26,24, Y2,22 and Z0,5. To determine whether points form the vertices of a right…

Q: Consider the regular hexagon shown on the coordinate plane. (-2. 3.5) (2.3.5) (4,0) (4. 0) (-2,-3.5)…

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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

Q: Find the equation of the perpendicular bisector of side of the triangle having vertices A…

A: The triangle has vertices A (-1,-3),B(5,-3) and C(5,5) so to find the perpendicular bisectors let D,…

Q: find The angle of the triangle whose vertices are C(1,-2, 2) Points AC-1,0,2) B (2,1,1) A B

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Q: The cosine of the acute angle e between the diagonais of a quadriateral having vertices at (0,0,0),…

A: Given:

Q: A 3. 2 D C -5 -4 -3 -2 -1 -1 1 2 3 4 5 -2 -3 -4 -5 4,

A: Explanation and solutions is given below....

Q: Use dot product to find the interior angles at A, B, and C of the triangle defined by the three…

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Q: An angle is in standard position if its vertex is at the ________ and its initial side isalong the…

A: An angle is in standard position if its vertex is at the ________ and its initial side is along the…

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: If A is (- 8, 3) and B is (- 4, – 1), then the midpoint of AB is (_?, ?_).

A: We know that, mid point of a line segment joining the points x1,y1 and x2,y2 is given as Mid…

Q: Is a triange with the verticies A(7,1) B(0,4) and C(-4,-8) a right triangle yes or no?

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Q: Use dot product to find the interior angles at A, B, and C of the triangle defined by the three…

A: HINT:  To calculate the angle we need the following thing: cos(α) = A.BAB We need to calculate AB…

Q: Find the per meter rhombus with of p c-2,3),01,1) RC4-3),5Ci,-7)

A: Given,quadrilateral is not a rhombus In a rhombus all sides are equal Perimeter of any quadrilateral…

Q: circle passing through (a, b) and cuts orthogonally to circle x? + y? = p², is

A: Introduction :

Q: The midpoint of AB is M(1, -4). If the coordinates of AA are (−3,−6), what are the coordinates of…

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Q: Find the angle between in the two planes a = (1,2,3)and b =(4,-5,6)

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Q: Find the area of a triangle with the points A(1,0,0), B(0,1,0), C(0,0, 1) as it vertices by using…

A: Question: Find the area of the triangle with the points A1,0,0, B0,1,0, C0,0,1 as its vertices by…

Q: The midpoint of AB is at (-5, 3). If A = (4, -6), find В. B is:(

A: Mid point: If Ax1, y1 and Bx2, y2 are any two points then, the coordinates of the midpoint of AB are…

Q: Consider a triangle with vertices A(1,0,0), B and C. Assume that • A : 1 • BC is parallel to the…

A: Given: A triangle with vertices A(1, 0, 0), B and C. BC is parallel to the y-axis and ||AB||=3

Q: Find the angle between in the two planes a = (1,2,3) and b =(4,-5,6)

A: Let's find angle between two plane.

Q: Use the dot proquct to find the largest interior angle of the triangle with vertices P(-1,2,3),…

A: We have given vertices of the triangle as P-1, 2, 3, Q1, 2, 1 and R2, 2, 1. First, we have to find…

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: Show that the points (a, a).(-a,-a) and (-3a, 3a) are the vertice of an equilateral triangle.Also,…

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Q: Find the angles of the triangle whose sides are x+y -4 = 0, 2x+y-6=0 and 5x+3y - 15 = 0.

A: Lines:x+y-4=0⇒y=4-x                      (1)2x+y-6=0⇒y=6-2x                  (2)5x+3y-15=0⇒y=153-53x…

Q: Find the distance in between the point P(0, 2, – 4) and the point Q(3, – 2, – 3). -

A: Given:P0,2,-4 and Q3,-2,-3

Q: 6a, YZ = 7a-3, XW=a, and WZ= a+

A: It is given that, In triangle XYZ, YW bisects angle XYZ

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: Show that the triangle whose vertices are A(-2, -3), B(4, 5), and C(-4, 1) is a right triangle.

A: Given:A-2,-3B4,5C-4,1Right triangle:AC2 =AB2+BC2

Q: Find the interior angles of the triangle whose vertices are A (-3, -2), B (2, 5) and C (4, 2).

A: Vertices of the triangle are given.we will find the angle of the triangle.Below find the solution in…

Q: In rhombus JKLM diagonals JL and KM are drawn. If JL = 12 and KM = 16, what is the perI! of JKLM?

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Q: if A(1,2,-1), B(3,6,-7), c(2,3,-3), D(3,4,-3) cotculate the angle between the voctar projection of…

A: Given points are                                 A(1, 2, -1), B(3, 6, -7), C(2, 3, -3), D(3, 4, -3)…

Q: Show that the two triangles are similar. Y

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Q: Prove that the midpoint of the hypotenuse of any right triangle is equidistant from the vertices.…

A: To solve the given problem

Q: Show that the points A(-4,9,6) ,B(-1,6,6) and C (0,7,10) from the right angled isoseles triangle

A: Use the equation D=(x2-x1)2+(y2-y1)2+(z2-z1)2 to calculate the magnitude of side AB.…

Q: Let ä = (4, 3) and b = (- 3, k). Find k so that ä and & will be orthogonal (form a 90 degree angle).

A: Given,            a→=<4,3>            b→=<-3,k>We know that,          For orthogonal,…

Q: Transform the triangle with the rule (x,y)→(x+2,y-4)

A: From figure, it is clear that the points of the triangles are as given below (1,3),(2,1) and (5,4)

Q: If A = (5, 1), B = (1,-3) and C= (2,-4), find the cosine of 2CAB. Let A = (-3, 2), B= (1, 0) and C=…

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Q: If AB = i + 4j – 2k and B is the point (5, 1, 3), find A. -

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Q: P, Q and How far is the point S from the plane that contains the points R?

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Given the midpoint M of the segment connecting A and B, find the missing coordinate. 6. А(х, 6),…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: -When rotating the triangle (abc) by 30° about the origin, where a-(1,1), b-(4,1) & e-4,3), the new…

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