6. Let ABCD be a trapezoid with bases BC and AD. A line passing through the vertex C and parallel to the diagonal BD of ABCD intersects the line through the base AD at the point M. Prove the triangle A ACM has the same area as the trapezoid.

Q: Consider the triangle with vertices in the points D(-5,0,5), E(2, 1,3), and C(3, 1,4). Compute the…

A: Vertices of triangle D(-5, 0,5) , E(2, 1,3) and C(3, 1,4) . We have to compute the area of triangle…

Q: 1. If (0, 0), (3, 0) and (x, y) are the vertices of an equilateral triangle, find x and y.

A:

Q: 56. Show that the six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1)…

A: Plotting given six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1).…

Q: thus. d the point on he sphere X+y?+=4 Selution:- ans.-

A: We use Lagrange Multiplayer method.

Q: ( , s) Let A = (-1,3) and B = (2, 4). Find the set of points C such that the area of triangle ABC is…

A:

Q: 4. Show that the two internal bisectors and one external bisector of the angles of a triangle meet…

A: Given:

Q: If D is the triangle with vertices (0,0), (40,0), (40,25), then dA=

A: The triangle D is with the vertices (0,0), (40,0) & (40,25). The line passing through (0,0) and…

Q: The points A, B, C and D represent the numbers Z₁, Z2, Z3 and z4 and O is the origin. 9 (a) If OABC…

A: We have to find value of Z3

Q: Example Give quadrilateral ABCD with verticesA(4, 7), B(8, 3), C(6,-1), andD(0, 5). Prove: ABCD is a…

A: Given : Quadrilateral ABCD with vertices A(4,7),B(8,3),C(6,-1) and D(0,5). So, Graph is :

Q: Show that a triangle with vertices at A(−1, 2), B(4, 1), and C(5, 6) is isosceles. Distance from…

A:

Q: Consider a right triangle whose sides are under the coordinate axes and the hypotenuse under the…

A: Tangent line and maximization area

Q: 5. The vertices of parallelogram ABCD are: A(3, -2, 4), B(-2, 0, 5), C(3, -5, -4) & D(x, y, z). a)…

A:

Q: Let vertices of an acute-angled triangle are A(z₁), B(z₂), and C(23). If the origin O is the…

A:

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

A:

Q: Evaluate ry dr +r dy, where C is the positively oriented triangle enclosed by the lines y = I=0 and…

A:

Q: 2. It is possible for two angles of a triangle in the hyperbolic plane to each have a measure of 2.

A: Solution

Q: Find the coordinates of the midpoint of the segment that joins the points a) (a, 0) and (0, b). b)…

A: Givena a, 0 and 0, bb 2a, 0 and 0, 2bMidpoint =x1 +x22 , y1+y22

Q: The triangle formed by A(z₁), B(22) and C(23) has its circumcentre at origin. If the perpendicular…

A:

Q: The triangle formed by A(z₁), B(z2) and C(z3) has its circumcentre at origin. If the perpendicular…

A:

Q: 4) The coordinates of the vertices of triangle SUE are S(-2,-4, Y(2,-1), and E(8,-9). Using…

A: