The three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of the fourth vertex.
ABCD is a parallelogram where A(x, y), B(5, 8), C(4, 7) and D(2, -4). Find
1) Coordinates of A
2) An equation of diagonal BD
Let A(-a, 0), B(0, a) and C(α , β) be the vertices of the L1 ABC and G be its centroid . Prove that
GA2 + GB2 + GC2 = `1/3` (AB2 + BC2 + CA2)
Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid point of AB is (2, 3). Find the values of x and y.
The centre ‘O’ of a circle has the coordinates (4, 5) and one point on the circumference is (8, 10). Find the coordinates of the other end of the diameter of the circle through this point.
The midpoint of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a+1). Find the value of a and b.
show that the points A(- 1, 2), B(2, 5) and C(- 5, – 2) are collinear.
M is the mid-point of the line segment joining the points A(-3, 7) and B(9, -1). Find the coordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p : q, find the ratio p : q