Find the distance of the following points from the origin:
If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Let A(2,−3)andB(−2,1) be the vertices of ABC˙ If the centroid of the triangle moves on the line 2x+3y=1, then find the locus of the vertex C˙
See Fig.3.14. and write the following:(i) The coordinates of B.(ii) The coordinates of C.(iii) The point identified by the coordinates (3, 5).(iv) The point identified by the coordinates (2, 4)˙ (v) The abscissa of the point D. (vi) The ordinate of the points H. (vii) The coordinates of the points L. (viii) The coordinates of the point M.
If (x,y) and (x,y) are the coordinates of the same point referred to two sets of rectangular axes with the same origin and it ux+vy, where u and v are independent of xandy , becomes VX+UY, show that u2+v2=U2+V2˙