Prove that the points 3,0),(4, 5),(-1, 4) and (-2,-1) taken in order, Lorm a rhombus, also find its area.

Q: Consider the shape with vertices (1,3),(4,7),(0,10),(-3,5) translate the rectangle so (1,3) lies on…

A: We need to transform the coordinates.

Q: Find the area of the triangle in the plane with vertices (3, 2), (7,3), and (6, -7). Area = 0

A:

Q: Find the area of the hyperbolic (geodesic) triangle with vertices (3,0), (4,0) and (5,0).

A: Let P(3,0), Q(4,0) and R(5,0) be three vertices.  It is known that the equation of hyperbolic line…

Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: Find the area of the quadrangle with vertices Area = (5,1). (-4, 5). (-3,-4), and (4, -3).

A:

Q: Find the area of the parallelogram with vertices at (5, -2), (11, 3), (14, –8), and (20, -3).

A:

Q: The triangle with vertices A(0, 1, 2), B(-1,0,2) and C(1,-2,0) has area = (ii)

A: A(0,1,2) B(-1,0,2) C(1,-2,0)

Q: Find the area of the parallelogram with vertices at (3, –3), (11, 1), (12,-5), and (20, –1). Area =

A:

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.…